# Function Operations Chapter Exam

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### Page 1

#### Question 1 1. What is g(f(4)) if g(x) = x+1 and f(x) = √(x)?

#### Question 2 2. Use f(x) and g(x) to find f(x) + g(x): f(x) = -x + 5 and g(x) = 3x + 2

#### Question 3 3. What is f(g(w)) = ?

#### Question 4 4. Which of the following describes the 'composite' of two functions?

####
Question 5
5.
What is the composite of the function below and its inverse?

f(x) = (x-2)/3

f^(-1)(x) = 3x + 2

Note: f^(-1)(x) indicates the inverse of the function f.

### Page 2

#### Question 6 6. What is the domain of the f(g(x))?

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Question 7
7.
Use f(x) and g(x) to find g(x) - f(x).

Here, f(x) = -x + 5 and g(x) = 3x + 2.

#### Question 8 8. What notation do you use to show that you have an inverse function?

#### Question 9 9. Given the following graph, what is f(f(1))?

####
Question 10
10.
Find the domain of f(f(x)) if

f(x) = (x+1)/x

### Page 3

#### Question 11 11. Use the graph to find f(f(2)).

#### Question 12 12. Which of the following is a one-to-one function?

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Question 13
13.
Find the inverse function of f(*x*) = 1?

#### Question 14 14. What is f(x) * g(x)?

#### Question 15 15. Solve:

### Page 4

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Question 16
16.
If f(*x*) = 5 - 2*x* and g(*x*) = -4*x* + 2, find g(f(*x*)).

#### Question 17 17. Using the graph, find f(f(-2)).

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Question 18
18.
What is the range of the function *f(x)* = *x*^2?

#### Question 19 19. What is the inverse function of:

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Question 20
20.
For a function f(*x*), what is f-1 (3*f(*x*))?

### Page 5

#### Question 21 21. What is the domain of f(g(x))?

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Question 22
22.
Find the domain of the inverse function of:

f(x) = 1/(x-3)

#### Question 23 23. How many times do the answers of a one-to-one function repeat?

####
Question 24
24.
Find f(g(2)) if:

f(x) = x^2

g(x) = x^3

####
Question 25
25.
If *f(x)* = *x* and *g(x)* = 1 / *x*, what is the domain of *f(g(x))*?

### Page 6

#### Question 26 26. Which of the following graphs is correct for:

#### Question 27 27. Which of the following statements is true?

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Question 28
28.
Which of the following are true for a one-to-one function?

I. It has only one input for a given output.

II. It has only one output for a given input.

III. It is always a linear function.

#### Question 29 29. What is the range of f(g(x)) if f(x) = |x| and g(x) = cos(x)?

#### Question 30 30. What is the domain of the inverse function of:

#### Function Operations Chapter Exam Instructions

Choose your answers to the questions and click 'Next' to see the next set of questions. You can skip questions if you would like and come back to them later with the yellow "Go To First Skipped Question" button. When you have completed the practice exam, a green submit button will appear. Click it to see your results. Good luck!