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

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Question 1206001: Evaluate the function at the indicated values. (If an answer is undefined, enter UNDEFINED.)
f(x) = x3 + 8x; f(−2), f(−1), f(0), f(1/2)
If I am correct, f(0)=0

Click here to see answer by math_tutor2020(3817)

Question 1206002: Evaluate the piecewise defined function at the indicated values.
f(x) = 2 if x ≤ 4
4x − 3 if x > 4

Click here to see answer by ikleyn(52793)

Question 1206002: Evaluate the piecewise defined function at the indicated values.
f(x) = 2 if x ≤ 4
4x − 3 if x > 4

Click here to see answer by math_tutor2020(3817)

Question 1206071: Find the domain of the function. (Enter your answer using interval notation.)
f(x) = x + 8/x2 + 4
Click here to see answer by ikleyn(52793)

Question 1206070: Find the domain of the function. (Enter your answer using interval notation.)
f(x) = x4/x2 + x − 56

Click here to see answer by ikleyn(52793)

Question 1206069: Find the domain of the function. (Enter your answer using interval notation.)
f(x) = x + 4/x2 − 9

Click here to see answer by ikleyn(52793)

Question 1206073: Find the domain of the function. (Enter your answer using interval notation.)
g(t) = square root t2 + 1

Click here to see answer by ikleyn(52793)

Question 1206072: Find the domain of the function. (Enter your answer using interval notation.)
f(t) = square root of t + 9

Click here to see answer by ikleyn(52793)

Question 1206075: Find the domain of the function. (Enter your answer using interval notation.)
f(x) = x2/square root of 7 − x

Click here to see answer by josgarithmetic(39618)

Question 1206075: Find the domain of the function. (Enter your answer using interval notation.)
f(x) = x2/square root of 7 − x

Click here to see answer by ikleyn(52793)

Question 1206074: Find the domain of the function. (Enter your answer using interval notation.)
g(x) = square root 4 + x/7 − x
Click here to see answer by josgarithmetic(39618)

Question 1206068: Find the domain and range of the function. (Enter your answers using interval notation.)
f(x) = 2x, −5 ≤ x ≤ 7
Click here to see answer by ikleyn(52793)

Question 1206139: How do I find the domain to this function: f(x)=1/(x^2-4x-5)

Click here to see answer by josgarithmetic(39618)

Question 1206341: Suppose that the function h is defined, for all real numbers, as follows.

h(x) = {2 if x<1}, {1 if x=1}, {0 if x>1}
Graph the function h.
Click here to see answer by MathLover1(20850)

Question 1206420: Find the domain and range of the quadratic function whose graph is described.
The vertex is (1, -11) and the graph opens up.
Click here to see answer by ikleyn(52793)

Question 1206448: Which of the following relationships represents a function?
A.
(-5,0), (5,3), (-7,1), (5,5)
B.
(-5,4), (5,6), (-5,3), (2,2)
C.
(-5,4), (4,6), (-5,3), (1,2)
D.
(-5,5), (5,3), (-7,2), (2,3)

Click here to see answer by greenestamps(13200)

Question 1206531: The table of values represents a polynomial function f(x) . How much greater is the average rate of change over the interval [4, 7] than the interval [2, 5]?
X f(x)
2 39
3 4
125 287
5 549
6 935
7 1469
Click here to see answer by MathLover1(20850)

Question 1206605: the equation defines a one-to-one function f.
f(x) = 4x − 1
Verify that
f ∘ f −1
and
f −1 ∘ f
are both the identity function.
(f ∘ f −1)(x) = f(f −1(x))
(f −1 ∘ f)(x) = f −1(f(x))
Click here to see answer by MathLover1(20850)

Question 1207165: Chris has invented a new app for smart phones that two companies are interested in purchasing for a 2-year contract.
Company A is offering her $10,000 for the first month and will increase the amount each month by $5000.
Company B is offering $500 for the first month and will double their payment each month from the previous month.
Monthly payments are made at the end of each month. For which monthly payment will company B’s payment first exceed company A’s payment?
A. 6
B. 7
C. 8
D. 9

Click here to see answer by mananth(16946)

Question 1207185: Mrs. Robinson made the table below showing the yearly balance of her savings
account. Interest on the account compounds annually. Which of the following
describes the best model to be used for Mrs. Robinson’s data?
Year Balance in Dollars
0 $400
5 $463.71
10 $537.57
15 $623.19
20 $722.44
25 $837.51
A) a positive linear function
B) a positive quadratic function
C) an exponential growth function
D) a positive absolute value function
Click here to see answer by math_tutor2020(3817)

Question 1207313: State whether or not the given equations determines y as a function of x
1. X+Y=1
2. X^2 + y^2=1
3. Y^2=X^2
4. Y=√x
5. Y=+-√X
Click here to see answer by MathLover1(20850)

Question 1207313: State whether or not the given equations determines y as a function of x
1. X+Y=1
2. X^2 + y^2=1
3. Y^2=X^2
4. Y=√x
5. Y=+-√X
Click here to see answer by ikleyn(52793)

Question 1207410: If f(x) is a function whose domain is [-8,4], and g(x) = f(-2x), then what is the domain of g(x)? Express your answer in interval notation.
I tried multiplying the original domain by -2, which yields [-8,16], but that is incorrect. Can anyone help? Thanks in advance!
Click here to see answer by MathLover1(20850)

Question 1207468: Suppose that f(x) and g(x) are functions such that the range of f is [-5,3], and the range of g is [-2,1]. The range of f(x) * g(x) is [a,b]. What is the largest possible value of b?
Click here to see answer by ikleyn(52793)

Question 1207515: Suppose that the functions f an g are defined as follows.
f(x)=1/3x squared+2
g(x)= square root of x+4
find f+g and f*g. Then give their domains using interval notation.
Click here to see answer by josgarithmetic(39618)

Question 1207513: Suppose that the functions g an h are defined as follows.
g(x)=(-3+x)(-3+x)
h(x)=2-8x
A. find (g/h)(6)
B. Find all the values that are not in the domain of g/h.
Click here to see answer by josgarithmetic(39618)

Question 1207514: Suppose that the functions g an h are defined as follows.
f(x)=square root of 3x-5
g(x)=x-2
find f-g and f*g. Then give their domains using interval notation.
Click here to see answer by josgarithmetic(39618)

Question 1207856: A student writes the six complex roots of the equation z^6 + 2 = 0 on the blackboard.
At every step, he randomly chooses two numbers a and b from the board, erases them, and replaces them with 3ab − 3a − 3b + 4.
At the end of the fifth step, only one number is left. Find the largest possible value of this number.

Click here to see answer by ikleyn(52793)

Question 1208008: Identify the range of the function:
y = 2/3x + 1/3 domain: 4, 6, 8 ,12

Click here to see answer by mananth(16946)

Question 1208026: If f(x) = 3x^2 - Bx + 4, and f(-1) = 12, what is the value of B?

Let me give it a try.

Let x = -1 and f(-1) be 12.

3(-1)^2 - B(-1) + 4

12 = 3(-1)^2 -B(-1) + 4

12 = 3(1) + B + 4

12 = 3 + B + 4

12 = B + 7

12 - 7 = B

5 = B

You say?

Click here to see answer by josgarithmetic(39618)

Question 1208025: Given that f(x) = 1/x and (f/g)(x) = (x + 1)/(x^2 - x), find the function g.

Let me see.

I know that (f/x)(x) means f(x)/g(x).

I think the set up is this:

(1/x)/g(x) = (x + 1)/(x^2 - x)

I must find g(x).

You say?
Click here to see answer by math_tutor2020(3817)

Question 1208034: Find the range of f(x) = (x^2 + 2)/(x + 4) algebraically?
It is my understanding that the domain of f inverse is the range of f.

You say?
Click here to see answer by ikleyn(52793)

Question 1208065: Given the piecewise function, find A to D.
f(x) = piecewise function
3x if x does not equal 0 is the top portion of the function.
4 if x = 0 is the bottom portion of the function.

A. Find domain.
B. Find range.
C. Locate intercepts.
D. Is f continuous on its domain?

Click here to see answer by ikleyn(52793)

Question 1208066: Given the integer function f(x)= int(2x), find A to D.

A. Find domain.
B. Find range.
C. Locate intercepts.
D. If f continuous on its domain?
Click here to see answer by ikleyn(52793)

Question 1208067: Let f(x) be a piecewise function.
Top portion: 2x + 5 if -3 <= x < 0
Middle portion: -3 if x = 0
Bottom portion: -5x if x > 0

A. Find domain and range.
B. Locate intercepts.
C. Is f continuous on its domain?
Click here to see answer by Edwin McCravy(20056)

Question 1208122: This is a four-part question.

A. Suppose that the graph of a function f is known.Explain how the graph of
y = 4•f(x) differs from the graph of y = f(4x).

B. Suppose that the graph of a function f is known.Explain how the graph of
y = f(x) - 2 differs from the graph of y = f(x - 2).

C. Suppose that the graph of a function f is known.Explain how the graph of
y = 4•f(x) differs from the graph of y = (1/4)f(x).

D. Suppose that the graph of a function f is known.Explain how the graph of
y = f(x) + 2 differs from the graph of y = f(x + 2).

Click here to see answer by ikleyn(52793)

Question 1208152: Suppose that f(x) = 3x + 5 and g(x) = -2x + 15.

A. Solve f(x) greater than or equal to g(x)
B. Solve f(x) less than or equal to g(x)
C. Graph y = f(x) and y = g(x) and label the point that represents the solution to the equation f(x) = g(x).
Note: Is part C asking for the point where the two graphs meet?

Thank you....

NOTE: HOW DO I POST MATH PICTURES ON THIS WEBSITE? I have lots of geometry and later on trigonometry applications with pictures to post.
Click here to see answer by josgarithmetic(39618)

Question 1208151: Suppose that f(x) = 3x + 5 and g(x) = -2x + 15.

A. Solve f(x) = 0

B. Solve g(x) < 0

C. Solve f(x) = g(x)

Thank you....

NOTE: HOW DO I POST MATH PICTURES ON THIS WEBSITE? I have lots of geometry and later on trigonometry applications with pictures to post.
Click here to see answer by josgarithmetic(39618)

Question 1208156: Find domain of f(x)/g(x).

f(x) = sqrt{4 - x^2}

g(x) = sqrt{9 - x^2}
Click here to see answer by ikleyn(52793)

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