Questions on Algebra: Functions, Domain, NOT graphing answered by real tutors!

Tutors Answer Your Questions about Functions (FREE)

Question 1196484: If for all a and b, and the function is never equal to zero, find the value of f(5).
Click here to see answer by ikleyn(52793)

Question 1196482: A function f is defined for integers m and n as given: f(mn)=f(m)f(n)-f(m+n)+ 1001, where either m or n is equal to 1, and f(1)=2.
a) Prove that f(x)=f(x-1)+1001.
b) Find the value of f(9999).
Click here to see answer by ikleyn(52793)

Question 1196483: Given that and , find all possible values for the sum of the coefficients in the quadratic function g(x).
Click here to see answer by ikleyn(52793)

Question 1196503: Determine the value of k so that the function will be its own inverse.
Click here to see answer by josgarithmetic(39618)

Question 1196503: Determine the value of k so that the function will be its own inverse.
Click here to see answer by MathLover1(20850)

Question 1196503: Determine the value of k so that the function will be its own inverse.
Click here to see answer by ikleyn(52793)

Question 1196554: A definition of a function
Click here to see answer by math_tutor2020(3817)

Question 1196554: A definition of a function
Click here to see answer by MathLover1(20850)

Question 1196626: Given a function f of a real variable that satisfies the equation defined by x f(2-x)- 2f(x)=x^2+1 for all real x, determine f(x) in terms of x
Click here to see answer by ikleyn(52793)

Question 1196705: Evaluating Mathematical Function
f(x) = 2x-5, g(x) = 3x-4
d. f(x)/g(x)
Click here to see answer by josgarithmetic(39618)

Question 1196705: Evaluating Mathematical Function
f(x) = 2x-5, g(x) = 3x-4
d. f(x)/g(x)
Click here to see answer by ikleyn(52793)

Question 1196807: Kayla works a total of 40 hours each week at two part-time jobs. She works at a restaurant and earns $12 per hour and as a freelance blog editor where she earns $19 per hour.
a) Write a function f that inputs the number of hours Kayla works at the restaurant (x) and outputs the number of hours she can work as a freelance blog editor.
f(x)=?

b) Write a function g that inputs the number of hours she worked as a freelance blog editor (n) in a week and outputs the total amount of money she made from editing that week (in dollars).
g(n)=?

c) Which composite function produces values with a real-world meaning in this context? f∘g or g∘f?
d) Write the formula that defines the composite function you selected in part (c).
g(f(x))=?

Click here to see answer by ewatrrr(24785)

Question 1196874: Please help me with this problem. From what I know, if a function f(x) is going to have an inverse then f(x) must 1-to-1. However the function below is not 1-to-1, but the problem is asking for it's inverse.
Would appreciate your guidance.
Find the inverse of a function:

Click here to see answer by math_tutor2020(3817)

Question 1196940: Find f(k - 1) when f(x) = 4x^2 - 3x + 4
Answer key provided, nothing I attempt so far step wise gets me to the correct answer however.
Answer key says the answer is: "4k^2 - 11k + 11"
Click here to see answer by math_tutor2020(3817)

Question 1197062: Find the inverse of the function:
f(x) =-2/3x+5
Click here to see answer by greenestamps(13200)

Question 1197571: A Ferris wheel has a 40-foot radius and the center of the Ferris wheel is 44 feet above the ground. The Ferris wheel rotates in the CCW direction at a constant angular speed of 2 radians per minute. Jordan boards the Ferris wheel at the 3-o'clock position and rides the Ferris wheel for many rotations. Let
t represent the number of minutes since the ride started.
a) Write an expression (in terms of t) to represent the number of radians Jordan has swept out from the 3-o'clock position since the ride started.

b) How long does it take for Jordan to complete one full revolution (rotation)?

c) Write an expression (in terms of t) to represent Jordan's height above the center of the Ferris wheel (in feet).

d) Write a function f that determines Jordan's height above the ground (in feet) in terms of t.
Click here to see answer by Theo(13342)

Question 1197707: Which of the following functions, if any, is an odd function?
A) f(X)=3X^2+5
B) f(X)= absolute value of (X-2)
C) f(X)=cos(X)+7
Click here to see answer by Shin123(626)

Question 1197773: {(6, -6), (2, 2), (0, 8), (5, 2), (-5, 2)}
Is the relation a function?
--------------------------------------------------
{(8, -8), (-4, -8), (7, -1), (-7, -1)}
Is the relation a function?
--------------------------------------------------
{(-24, -141), (-9, -141), (133, -83), (-21, -83), (-9, -141), (133, -138)}
Is the relation a function?
Click here to see answer by josgarithmetic(39618)

Question 1197778: 7. y = x2 + 86
A. Domain = {all real numbers}, Range = {all real numbers < 86}
B. Domain = {all real numbers}, Range = {all real numbers >= 86}
C. Domain = {all real numbers}, Range = {all real numbers}
D. Domain = {all real numbers}, Range = {all real numbers <= 1}
E. Domain = {all real numbers <= 1}, Range = {all real numbers <= 86}
F. Domain = {all real numbers > 1}, Range = {all real numbers}

8. y = 2x3 + 8
A. Domain = {all real numbers}, Range = {all real numbers}
B. Domain = {all real numbers}, Range = {all real numbers > 8}
C. Domain = {all real numbers}, Range = {all real numbers >= 8}
D. Domain = {all real numbers}, Range = {all real numbers <= 8}
E. Domain = {all real numbers <= 2}, Range = {all real numbers <= 8}
F. Domain = {all real numbers > 2}, Range = {all real numbers}
Click here to see answer by math_tutor2020(3817)

Question 1197781: 13. f(x) = -13x2 - 7x4 - 11x
find f(5)
A. 538
B. -6288203
C. 639
D. -4595
E. -4,755
F. -3456

14. f(x) = 15x - 12
g(x) = -15x2 + 14x - 10
find g(g(7))
A. -6288203
B. 6543
C. 639
D. -4595
E. 538
F. -162,632
Click here to see answer by math_tutor2020(3817)

Question 1197780: 11. f(x) = 11x - 5x2 + 4
find f(-4)
A. 619
B. -4,755
C. -6288203
D. 639
E. -120
F. -4595

12. f(x) = 7 - 5x + 7x2
find f(-9)
A. 639
B. -4,755
C. -6288203
D. 619
E. -4595
F. 538
Click here to see answer by josgarithmetic(39618)

Question 1197779: 9. y = -9x + 11
A. Domain = {all real numbers}, Range = {all real numbers <= 11}
B. Domain = {all real numbers}, Range = {all real numbers > 11}
C. Domain = {all real numbers}, Range = {all real numbers > 0}
D. Domain = {all real numbers}, Range = {all real numbers}
E. Domain = {all real numbers <= 9}, Range = {all real numbers}
F. Domain = {all real numbers > 9}, Range = {all real numbers}

10. y = 40 - 8x2
A. Domain = {all real numbers <= 8}, Range = {all real numbers <= 40}
B. Domain = {all real numbers}, Range = {all real numbers > 40}
C. Domain = {all real numbers}, Range = {all real numbers}
D. Domain = {all real numbers}, Range = {all real numbers <= 40}
E. Domain = {all real numbers}, Range = {all real numbers <= 8}
F. Domain = {all real numbers > 8}, Range = {all real numbers}
Click here to see answer by math_tutor2020(3817)

Question 1197785: Find an equation of the line through the point (3 , 5) that is perpendicular to the line 2X+5Y=4
Click here to see answer by ewatrrr(24785)

Question 1197785: Find an equation of the line through the point (3 , 5) that is perpendicular to the line 2X+5Y=4
Click here to see answer by greenestamps(13200)

Question 1197811: 19. f(x) = 15x + 12
g(x) = -10x + 15
find f(g(8))
A. 639
B. -963
C. 178031
D. -5943
E. -524
F. -68203
Click here to see answer by MathLover1(20850)

Question 1197811: 19. f(x) = 15x + 12
g(x) = -10x + 15
find f(g(8))
A. 639
B. -963
C. 178031
D. -5943
E. -524
F. -68203
Click here to see answer by ikleyn(52793)

Question 1197810: 17. f(x) = 15x3 + 13x2 - 15x + 15
g(x) = 15x + 11
find g(f(9))
A. 639
B. -5943226
C. -52466
D. -6288203
E. 178031
F. -4595

18. f(x) = -13x2 - 13x + 14
g(x) = -13x - 11
find g(g(3))
A. 639
B. 178031
C. -5943226
D. -52466
E. -6288203
F. 752
Click here to see answer by ikleyn(52793)

Question 1197809: 15. f(x) = -13x2 + 12x + 14 g(x) = 11x - 13
find f(g(7))
A. -162,632
B. -6288203
C. 639
D. -4595
E. 538
F. -52466

16. f(x) = 11x + 15
g(x) = -11x3 - 15x2 + 13x - 13
find g(f(6))
A. -4595
B. -52466
C. -6288203
D. -5943226
E. 639
F. 538
Click here to see answer by ikleyn(52793)

Question 1197822: Let f(x)=[-x-3 , cubic root of x, x^2-x, x < -1, -1 < or equal x < 2, x > or equal 2
Find f(-1), f(1), and f(2)
Click here to see answer by math_tutor2020(3817)

Question 1197832: A high-technology electronics firm needs a special microprocessor for use in a microcomputer it manufactures. Three alternatives have been identified for satisfying its needs. It can
purchase the microprocessors from a supplier at a cost of $10 each. The firm also can purchase
one of two pieces of automated equipment and manufacture the microprocessors. One piece of
equipment costs $80,000 and would have variable costs per microprocessor of $8. A more highly
automated piece of equipment costs $120,000 and would result in variable costs of $5 per unit.
Determine the minimum cost alternative for different ranges of output
Click here to see answer by Theo(13342)

Question 1197833: 15. f(x) = -13x2 + 12x + 14 g(x) = 11x - 13
find f(g(7))
A. -162,632
B. -6288203
C. 639
D. -4595
E. 538
F. -52466

18- f(x) = -13x2 - 13x + 14
g(x) = -13x - 11
find g(g(3))
A. 639
B. 178031
C. -5943226
D. -52466
E. -6288203
F. 752
Click here to see answer by josgarithmetic(39618)

Question 1197835: State the inverse of each relation. Is the inverse a function?

1. {(18, -3), (-13, -10), (-3, 17), (0, -15)}
A. Inverse={(18, -3), (-15, 0), (-3, 16), (-10, -13)} The inverse is a function.
B. Inverse={(17, -3), (-15, 0), (-3, 18), (-10, -13)} The inverse is not a function.
C. Inverse={(17, -3), (-15, 0), (-3, 18), (-10, -13)}The inverse is a function.
D. Inverse={(18, -3), (-15, 0), (-3, 16), (-10, -13)} The inverse is not a function.
E. Inverse={(-18, 3), (13, 10), (3, -17), (0, 15)} The inverse is a function.
F. Inverse={(-18, 3), (13, 10), (3, -17), (0, 15)} The inverse is not a function.

2. {(5, -11), (-19, -19), (-6, -4), (-3, 8), (-12, 5)}
A. Inverse={(-4, -6), (-19, -19), (-11, 5), (5, -12), (8, -3)} The inverse is not a function.
B. Inverse={(-4, -6), (-19, -19), (-11, 5), (5, -12), (8, -3)} The inverse is a function.
C. Inverse={(5, 6), (19, 19), (11, -5), (-5, 12), (-8, 3)} The inverse is a function.
D. Inverse={(5, 6), (19, 19), (11, -5), (-5, 12), (-8, 3)} The inverse is not a function.
E. Inverse={(-5, -6), (-19, -19), (-11, 5), (5, -12), (-12, -3)} The inverse is a function.
F. Inverse={(-5, -6), (-19, -19), (-11, 5), (5, -12), (-12, -3)} The inverse is not a function.
Click here to see answer by ikleyn(52793)

Question 1197837: 5. {(-14, -9), (-0, 2), (8, -4), (-5, 6), (-7, -4)}
A. Inverse={(2, -0), (6, -5), (-4, 8), (-9, -14), (-4, -7)} The inverse is not a function.
B. Inverse={(2, -0), (6, -5), (-4, 8), (-9, -14), (-4, -7)} The inverse is a function.
C. Inverse={(14, 9), (0, -2), (-8, 4), (5, -6), (7, 4)} The inverse is not a function.
D. Inverse={(14, 9), (0, -2), (-8, 4), (5, -6), (7, 4)} The inverse is a function.
E. Inverse={(2, 0), (6, 5), (4, 8), (9, 14), (4, 7)} The inverse is not a function
F. Inverse={(2, 0), (6, 5), (4, 8), (9, 14), (4, 7)} The inverse is a function.

6. {(-15, -1), (0, -1), (-6, -1), (-16, 3)}

A. Inverse={(1, 15), (3, 16), (1, 0), (1, 6)} The inverse is a function.
B. Inverse={(-1, -15), (3, -16), (-1, 0), (-1, -6)} The inverse is a function.
C. Inverse={(15, 1), (-0, 1), (6, 1), (16, -3)} The inverse is not a function.
D. Inverse={(15, 1), (-0, 1), (6, 1), (16, -3)} The inverse is a function.
E. Inverse={(1, 15), (3, 16), (1, 0), (1, 6)} The inverse is not a function.
F. Inverse={(-1, -15), (3, -16), (-1, 0), (-1, -6)} The inverse is not a function.
Click here to see answer by ikleyn(52793)

Question 1197836: 3. {(-9, -8), (-16, 5), (17, 6), (19, 4), (-8, 9), (-10, -10)}
A. Inverse={(5, 16), (9, 8), (-10, 9),(-8, -9), (4, 19), (-6, 17)} The inverse is a function.
B. Inverse={(5, -16), (9, -8), (-10, -10),(-8, -9), (4, 19), (6, 17)} The inverse is not a function.
C. Inverse={(9, 8), (16, -5), (-17, -6), (-19, -4), (8, -9), (10, 10)} The inverse is a function.
D. Inverse={(9, 8), (16, -5), (-17, -6), (-19, -4), (8, -9), (10, 10)} The inverse is not a function.
E. Inverse={(5, -16), (9, -8), (-10, -10),(-8, -9), (4, 19), (6, 17)} The inverse is a function.
F. Inverse={(5, 16), (9, 8), (-10, 9),(-8, -9), (4, 19), (-6, 17)} The inverse is not a function.

4. {(8, -5), (-4, -14), (16, 12), (-13, 4), (-17, -2), (3, -13)}
A. Inverse={(-8, 5), (4, 14), (-16, -12), (13, -4), (17, 2), (-3, 13)} The inverse is not a function.
B. Inverse={(-14, -4), (-13, 3), (4, -13), (12, 16), (-5, 8), (-2, -17)} The inverse is not a function.
C. Inverse={(-8, 5), (4, 14), (-16, -12), (13, -4), (17, 2), (-3, 13)} The inverse is a function.
D. Inverse={(-14, -4), (-13, 3), (4, -13), (12, 16), (-5, 8), (-2, -17)} The inverse is a function.
E. Inverse={(-4, -4), (-13, 3), (4, -13), (14, 16), (5, 8), (-2, -17)} The inverse is a function.
F. Inverse={(-4, -4), (-13, 3), (4, -13), (14, 16), (5, 8), (-2, -17)} The inverse is not a function.
Click here to see answer by ikleyn(52793)

Question 1197856: Let f(X)=[-x-3 , x<-1 , cubic root of x , -1<=x<2 , x^2-x , x>=2].Find f(-1) , f(1) , f(2)
Click here to see answer by MathLover1(20850)

Question 1197856: Let f(X)=[-x-3 , x<-1 , cubic root of x , -1<=x<2 , x^2-x , x>=2].Find f(-1) , f(1) , f(2)
Click here to see answer by math_tutor2020(3817)

Question 1197895: Find the composition of functions indicated:
1. g[f(x)] if g(x) = x2 and f(x) = x + 3.
A. x2 + 6x + 9
B. x2 + x + 3
C. x2 - x - 3
D. x3 + 3x2
E. x2 + 3
F. x2 + 9

2. f[g(x)] if g(x) = x2 and f(x) = x + 3.
A. x2 + 6x + 9
B. x2 + 3
C. x3 + 3x2
D. x2 + x + 3
E. x2 - x - 3
F. x2 + 9

3. g[f(x)] if f(x) = 4x + 1 and g(x) = 2x2 - 5
A. 8x2 - 19
B. 8x3 + 6
C. 16x2 + 8x - 2
D. 8x2 - 20
E. 16x2 + 8x - 20
F. 32x2 + 16x - 3

4. f[g(x)] if f(x) = 4x + 1 and g(x) = 2x2 - 5
A. 32x2 + 16x - 3
B. 8x3 + 6
C. 16x2 + 8x - 2
D. 8x2 - 19
E. 8x2 - 20
F. 16x2 + 8x - 20

5. g[f(x)] if g(x)=√(x) and f(x)= x + 1
A. √(x + 1)
B. √(x) + 1
C. x2 + 1
D. x2 + x + 1
E. x2 + x
F. x + 1

6. f[g(x)] if g(x)=√(x) and f(x)= x + 1
A. √(x + 1)
B. x2 + 1
C. √(x) + 1
D. x2 + x
E. x + 1
F. x2 + x + 1

7. s[h(x)] if s(x) = 2x and h(x) = x2
A. 4
B. 2(x2)
C. 4x
D. x(2x)
E. x2
F. 2x2

8. h[s(x)] if s(x) = 2x and h(x) = x2
A. (2x)2
B. 4
C. 42x
D. x(2x)
E. x2
F. 2x2

9. n[m(t)] if n(x) = 3x and m(t) = √(t) + 1
A. √(3x) + 1
B. 3[√(t)]
C. √(t) + 3
D. 3[√(t) + 1]
E. 3[√(t)] + 3
F. √(3x) + 3

10. m[n(x)] if n(x) = 3x and m(t) = √(t) + 1
A. 3[√(t) + 1]
B. 3[√(t)] √(t) + 3
C. √(t) + 3
D. √(3x) + 1
E. √(3x) + 3
F. 3[√(t)] + 3
Click here to see answer by MathLover1(20850)

Question 1197899: Solve:
16. f(x) = 12x2 + 11x - 15
g(x) = 10x + 15
find g(g(9))
A. 2324
B. 2064
C. 1077
D. 1065
E. 1056
F. 1234

17. f(x) = -14x2 - 14x + 11
g(x) = -14x2 + 14x + 12
find g(f(3))
A. 356785
B. -356786
C. 3456345
D. -342553
E. -347272
F. -324564
Click here to see answer by MathLover1(20850)

Question 1197901: Find the composition of functions indicated:

7. s[h(x)] if s(x) = 2^x and h(x) = x^2
A. 4
B. 2^(x2)
C. 4^x
D. x^(2x)
E. x^2
F. 2x^2
Click here to see answer by MathLover1(20850)

Question 1197898: For the following, find the composition of functions (fog)(x).
11. g(x) = 3x, f(x) = x + 1
A. 3x(x + 1)
B. 4x + 1
C. 3(x)2 + 1
D. 3(x + 1)
E. 3x + 1
F. x(x + 1)

12. g(x) = (2x) (1/2), f(x) = x2 + 1
A. 2x + (1/2)
B. (x2 + 1)
C. 2(x2)
D. 2x + 1
E. (x2 + 1)(2x)
F. (x2 + 1)(2x)1/2

13. g(x) = 3/(x - 1), f(x) = (x - 1)/(x - 3)
A. (x - 1)/(x - 3) * 3/(x - 1)
B. (x - 1)/(x - 1) * 3/(x - 1)
C. (x - 4)/(x - 2)
D. (x - 4)/(3x - 3)
E. (x - 4)/(3x - 6)
F. 3x2

14. g(x) = x2 - 8, f(x) = (-x + 1)1/2
A. (-x2 + 9)(1/2)
B. (-x2 - 8)(1/2)
C. (-x + 1)(1/2) (x2 - 8)
D. (-x + 1)(1/2) (x2 - 8)
E. (-x2 - 9)(1/2)
F. (x - 2)2

15. g(x) = (x2 -16)(1/2), f(x) = (3 - x)(1/2)
A. (3 - x)(1/2), (x2 -16)(1/2)
B. (-x-13)(1/2)
C. (3-(x2 -16)(1/4))
D. (3x2 + 16)
E. (3x(1/2) + 16)
F. (3-(x2 -16)(1/2))(1/2)
Click here to see answer by MathLover1(20850)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660