Question 1

Given $$f(x) = \frac{5}{2x-1}$$ and $$g(x) = 2x-3$$, what is $$f(g(x))$$?

Accepted Answer

$$\frac{5}{4x-7}$$

Question 2

What is the domain of $$f(g(x))$$ where $$f(x) = \frac{5}{2x-1}$$ and $$g(x) = 2x-3$$?

Accepted Answer

$$x 
eq 1.75$$

Question 3

Given $$f(x) = \frac{1}{x-5}$$, find $$f^{-1}(x$$)$$.

Accepted Answer

Question 4

Are $$f(x) = \frac{x+1}{x-1}$$ and $$g(x) = \frac{x-1}{x+1}$$ inverses of each other? Show algebraically using composition.

Accepted Answer

Yes, because $$f(g(x)) = x$$ and $$g(f(x)) = x$$

Question 5

Simplify $$16^{1/4}.$$

Accepted Answer

$$2$$

Question 6

Simplify $$6^{1/2}$$ \cdot $$6^{3/2}.$$

Accepted Answer

$$36$$

Question 7

Simplify $$e^{2x}$$ \cdot $$e^{3x}.$$

Accepted Answer

$$e^{5x}$$

Question 8

Which of the following is the correct graph for $$y = 2 + e$$^{x}$$?

Accepted Answer

An exponential curve shifted up by 2 units

Question 9

Explain what a 1-1 function is and why a function must be 1-1 to have an inverse.

Accepted Answer

A 1-1 function assigns each input to a unique output, so only these functions have inverses.

Question 10

Simplify $$\left(\frac{a^3$}{b^2$}\$$right)^{-2}$$.

Accepted Answer

$$\frac{b^4$}{a^6$}$$

Question 11

Simplify $$(-3a^2bc$$^{-1}$$)^2.$$

Accepted Answer

$$9a^4b^2$c^{-2}$$

Question 12

If $$f(x) = 2x + 1$$ and $$g(x) = x^2$, what is f(g(3$$))$$?

Accepted Answer

$$19$$

Question 13

Which of the following is NOT a property of exponential functions?

Accepted Answer

Their graphs always pass through the origin.

Question 14

If $$f(x) = \frac{1}{x}$$, what is the domain of $$f^{-1}(x$$)$$?

Accepted Answer

$$x 
eq 0$$

Question 15

Which of the following is the inverse of $$f(x) = 3x + 2$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x-2}{3}$$

Question 16

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is f(g(9$$))$$?

Accepted Answer

$$9$$

Question 17

Which of the following is true about the composition $$f(g(x))$$?

Accepted Answer

The domain of $$f(g(x)) is $$all $$x$$ such that $$g(x) is in $$the domain of $$f.$$

Question 18

Which of the following is a necessary condition for a function to have an inverse?

Accepted Answer

The function must be one-to-one.

Precalculus Study Notes: Functions, Inverses, and Exponents

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