# Understanding Function Operations in Trigonometry: Help and Review Chapter Exam

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!

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#### Question 1 1. Which function would NOT pass the horizontal line test?

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Question 2
2.
Find the inverse function of:

y = 1/x

#### Question 3 3. What is g(f(4)) if g(x) = x+1 and f(x) = √(x)?

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Question 4
4.
If f(x) = x^2 and g(x) = x + 1, what is f(g(x))?

Hint: For every *x* in f(x) put in g(x)

*x*in f(x) put in g(x)

#### Question 5 5. If f(x) = -2x -5 and g(x) = x^2 + 1, find f(g(x)).

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#### Question 6 6. While reading your textbook, you find a function that has two inputs that produce the same answer. Based on this information, you know that this function is _____.

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Question 7
7.
Solve the following equation for c.

2a - 3b + c - 3 = 6a + 4b - 12

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

#### Question 9 9. Using the graph, find f(f(-2)).

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Question 10
10.
Find f(g(2)) if:

f(x) = x^2

g(x) = x^3

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Question 11
11.
What is the domain of the function *f(x)* = *x*?

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Question 12
12.
Find the domain of the inverse function of:

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

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Question 13
13.
Find the domain of f(f(x)) if

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

#### Question 14 14. What is the range of f(g(x)) if f(x) = |x| and g(x) = cos(x)?

#### Question 15 15. If f(x) = 5 + 3x and g(x) = 5 - 9x, find f(g(2)).

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#### Question 16 16. If f(x) = -2x - 5 and g(x) = x^2 + 1, find f(f(x)).

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Question 17
17.
Recalling function notation, we want *x* to be *w*. Therefore, if f(x) = (3x + 5) / 2, find f(w).

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Question 18
18.
For a function f(*x*), what is f - 1 (3 * f(*x*))?

#### Question 19 19. What is f(2) if f(g(3)) = 1 and g(x) = x-1?

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Question 20
20.
Find the domain of f(g(x)), if:

f(x) = 1/x

g(x) = 1/(x+4)

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#### Question 21 21. How many times do the answers of a one-to-one function repeat?

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

f(x) = 2x + 1

#### Question 23 23. Which of the following is the inverse function of f(x) = 2x - 3?

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Question 24
24.
What is the domain of *f(x)* = 1 / *x*?

#### Question 25 25. All of the following are one-to-one functions, EXCEPT:

### Page 6

####
Question 26
26.
Solve for x and y.

x + y = 5

x - y = -1

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Question 27
27.
What is the range of the function *f(x)* = *x*^2?

#### Question 28 28. Which of the following statements best describes the 'composite' of two functions?

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Question 29
29.
Find the inverse function of f(*x*) = 1?

#### Question 30 30. Which of the following is the inverse function of f(x) = 3x?

#### Understanding Function Operations in Trigonometry: Help and Review 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!