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

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Question 1188552: 1.The amount of copper ore produce from a copper mine in Arizona is modeled by the function (x)=200+32x
Where x is the number of year's since 2005, and f(x) is measured in thousands of tons.
a. Sketch the graph of f.
b. What is slope of the graph?
c. At what rate is the amount of ore produced changing?
2. Find two positive real numbers whose sum is 40 and who's product is maximum.
Click here to see answer by Boreal(15235)

Question 1188551: Given the function f(x)=3x²-4x=2, g(x)=x+13, and h(x)=square root of x minus 12, perform the indicated operations.
a. (f+g)(x)
b. (f+h)(x+2)
c. (f•g•h)(x)
d. (f/g)(x)
Click here to see answer by Alan3354(69443)

Question 1188577: Let f(x)= √x. Find g(x), the function that is f(x) shifted up 10 units and left 9 units
Click here to see answer by ikleyn(52794)

Question 1188640: Is {(x, y)| y^4 = x − 3} a function?
Click here to see answer by ikleyn(52794)

Question 1188659: Hello,
I would like help putting getting the domain and range for this set of data
Temp Ice Cream Sales
80 $200
79 $215
68 $100
84 $250
89 $320
87 $300
75 $130
73 $120
79 $150
92 $400
94 $420
93 $400
87 $380
60 $70
40 $30

Click here to see answer by Boreal(15235)

Question 1188797: what is the inverse of f(x)=5-2x?
Click here to see answer by MathLover1(20850)

Question 1188797: what is the inverse of f(x)=5-2x?
Click here to see answer by Alan3354(69443)

Question 1188797: what is the inverse of f(x)=5-2x?
Click here to see answer by greenestamps(13200)

Question 1188984: Find f^−1(x)for f(x)=23/x^2,x>0.
Click here to see answer by greenestamps(13200)

Question 1189168: Each year, a baseball team sells boxes of chocolates as a fundraiser to lower the cost of team fees. The price of the chocolates and the number of boxes sold varies each year. The information from five years of sales are given in the table below.
Price per box ($) 3.00 4.00 5.50 6.50 8.00
Boxes sold 5837 3571 1950 1409 1118
a. Find the regression equation in the form 3 2 y ax bx cx d = + ++ that best approximates the
data. Express the values of a, b, c, and d to the nearest hundredth.
b. Use the equation to find the number of boxes, to the nearest whole number, that the team will sell if they charge $4.35 per box.
c. One year, the team only sold 366 boxes of chocolates. What price did they charge for each
box?
d. If the team raises the price too high, they will not sell any boxes. Use your regression equation to predict the price of a box that will result in zero boxes sold.
Click here to see answer by math_tutor2020(3817)

Question 1189255: Find k so that the minimum value of f(x) = x^2 + kx + 8 is equal to the maximum value of g(x) = 1 + 4x -2x^2
Click here to see answer by ikleyn(52794)

Question 1189255: Find k so that the minimum value of f(x) = x^2 + kx + 8 is equal to the maximum value of g(x) = 1 + 4x -2x^2
Click here to see answer by Solver92311(821)

Question 1189267: The weight w( in kilograms ) of a milkfish is related to its length l (in centimeters ) by this function : w = (9.37×10⁶)L3.Find the inverse of the function . Then determine the approximate length of hake that weighs o.679 kilogram.
Click here to see answer by ikleyn(52794)

Question 1189271: Determine whether each statement is true or false. Show your solution to prove your answer.
1. If f(x)=x-4 and g(x)= x+5,then (f-g)(x)=2
2. If f(x)=5x-4 and g(x)= 3x+5, then (f+g)(x)=8x+1
3. If f(x)=5x-4 and g(x)= 3x+5, then (fg)(x)=5x+4
Click here to see answer by MathLover1(20850)

Question 1189264: a) For the given functions 𝑓(𝑥)= x/x-1 and g(x)=-4/x ,find the domain of the
composite functions 𝑓o𝑔 and 𝑔o𝑓.
b) Is 𝑓(𝑥)=x^3 invertible? Explain with reason.
If 𝑓(𝑥) is invertible, find the inverse of 𝑓(𝑥). Also, graph 𝑓 and 𝑓^-1 on the
same coordinate axes.

Click here to see answer by MathLover1(20850)

Question 1189270: As part of boosting your health this time of pandemic, you ask your parent if you could enroll at a Zumba class that was held online. Your parent agreed to it and the Zumba instructor said that she charges according to the number of participants. This is the list of charges that she said,if there are 20 participants or below, the instructor charges ₱400.00 for each participant per month. If the number of participant is between 20 and 30, she charges ₱350.00 for each participant per month. If there are 30 participants or more she charges ₱300.00 for each participants per month. Write the piecewise function that describes what the instructor charges .
Click here to see answer by math_tutor2020(3817)

Question 1189269: Dalia,Ruth and Amy go to the store to buy snacks. Delia buys 3 oranges and 3 apples. Ruth buys 1 banana, 2 oranges and 3 apples. Amy buys 2 bananas and 4 oranges . Delia's bill comes to ₱13.72, Ruth's to ₱15.06, and Amy to ₱16.58.How much does one orange cost?
Click here to see answer by ikleyn(52794)

Question 1189334: 1. Given f(x)=3x^4 -2x^3 + 7x -2, how many sign changes are there in the
coefficient of f(-x)?

Click here to see answer by MathLover1(20850)

Question 1189334: 1. Given f(x)=3x^4 -2x^3 + 7x -2, how many sign changes are there in the
coefficient of f(-x)?

Click here to see answer by greenestamps(13200)

Question 1189349: Please check the document out:
https://docs.google.com/document/d/1ELpsYiSz9SEXTm8wbhrc8E2lS_mr2YME6ihRbBIhlMo/edit?usp=sharing
I got k=4 somehow.
Click here to see answer by ikleyn(52794)

Question 1189361: Define composite functions. For the functions f(x)= x/x+3 and g(x)= 2/x,find f ◦ g
,Also determine the domain for this new function.

Click here to see answer by greenestamps(13200)

Question 1189363: 1 a)Is the function f(x) = x^2 +9,x ≥ 0 one-to-one? If so, find f^-1 and justify your answer.
b)Graph f, f^−1,and y=x on the same coordinate axes. Also state domain and range of f and f^-1.
.
Click here to see answer by ikleyn(52794)

Question 1189765: f(x)=-3(x-5)^2 +8 Evaluate a) f^-1(x)
Click here to see answer by ikleyn(52794)

Question 1189760: For each pair of functions f and g below, find f (g (x)) and g (f(x))
Then, determine whether f and g are inverses of each other.
Simplify your answers as much as possible.
(Assume that your expressions are defined for all x in the domain of the composition.
You do not have to indicate the domain.)
(a) f(x) =1/4x , x ≠ 0
g(x) = 1/4x , x ≠ 0
f(g(x))=
g(f(x))=
are f and g inverses of each other? yes or no?

(b) f(x)=x+6
g(x)=x+6
f(g(x))=
g(f(x))=
are f and g inverses of each other? yes or no?
Click here to see answer by Theo(13342)

Question 1189771: Suppose that the functions g and f are defined as follows. g(x)=x-8, f(x) = (x-3)(x-5)
(a) Find (g/f)(1)
(b) Find all values that are NOT in the domain of If there is more than one value, separate them with commas.
Click here to see answer by MathLover1(20850)

Question 1189873: 1. Richard has available 400 yards of fencing and wishes to enclose a rectangular area.
a.) Express the area A of the rectangle as a function of the width x of the rectangle?
b.) What is the domain of A?
Click here to see answer by ikleyn(52794)

Question 1189906: Consider the function f:R~R is given by x^2y+y=6.
(1) find an explicit formula for f
(2) what is the domain
(3) state any three integer which are not in the range of f
(4) obtain a formula for f^-1
(5) compute f^-1(5)
(6) For what value(s) of x is f^-1 undefined
(7) for what value(s) of x is f^-1 zero
Click here to see answer by MathLover1(20850)

Question 1189931: f(x)=h(3x^2+1). Find fَ(1) if hَ(1)=5 and hَ(4)=2.
Click here to see answer by ikleyn(52794)

Question 1190559: How much money should be invested at 5% compounded quarterly for
20 years so that you have P20,000 at the end of 20 years?

Click here to see answer by ikleyn(52794)

Question 1190558: How much money should be invested at 5% compounded quarterly for
20 years so that you have P20,000 at the end of 20 years?

Click here to see answer by ikleyn(52794)

Question 1190587: Find the tangent to f(x) = x^2 at the point where
i. x= 1
ii. x= 4
Please explain step-by-step!
Click here to see answer by math_tutor2020(3817)

Question 1190590: Use limits to find the slope of the tangent to f(x) = x^2, at the point (3,9).
Please use the differentiation from the first principles method if possible, as I don't understand how it would work here.
Click here to see answer by math_tutor2020(3817)

Question 1190715: An airplane is flying at a speed of 250 mph at an altitude of 5 miles. The plane passes directly above a radar station at time t = 0.
Find the distance s between the plane and the radar station after 5 minutes.
Click here to see answer by ikleyn(52794)

Question 1190718: Find the domain of gf if f (X) =x^2 and g(X) = square root of x-6
Click here to see answer by ikleyn(52794)

Question 1190826: Given the functions f(x)=1/x Write the equation g(x) after the following transformations,
Horizontal compression by the factor of 1/5
Vertical stretch by the factor of 7
Reflection in the y-axis
Translation 11 units left and 9 unit down

Click here to see answer by Solver92311(821)

Question 1190856: Find the derivative function (dy/dx) for y=1/(5-2x).
Click here to see answer by math_tutor2020(3817)

Question 1190912: Explain the transformations you would need to apply to the graph of y=f(x) to graph the function

y=-f(1/4x+6) -7
Click here to see answer by greenestamps(13200)

Question 1190934: The tangent to the curve y = 2x^2 + ax + b at the point (-2,11) is perpendicular to the line 2y = x + 7. Find the value of a and b.
Click here to see answer by math_tutor2020(3817)

Question 1190979: F(-2) = 3 and g(-2) = -7 find the following
(F+g) (-2)
Click here to see answer by Alan3354(69443)

Question 1191029: Write an equation in standard form of the ellipse described. The center of the ellipse is the origin.
Major axis of length 16 units located on the y-axis and minor axis of length 12 units

Click here to see answer by ikleyn(52794)

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