Q: Determine if $$F(x) = 2x - 1$$ and $$G(x) = -2x + 1$$ are inverses. Explain your answer.

No, because $$F(G(x)) \neq x$$ and $$G(F(x)) \neq x$$

Question 1

Simplify $$3^2$$ - $$3^3. $$What is the result?

Accepted Answer

$$-18$$

Question 2

Which of the following is the correct simplification of $$(-27)^{\frac{4}$${3}}$$?

Accepted Answer

$$81$$

Question 3

What is the value of $$\log_7$ 49$$?

Accepted Answer

$$2$$

Question 4

Solve for $$x$$: $$2^{3x}$$ = $$4^{x+1}$$

Accepted Answer

$$x = 1$$

Question 5

Which of the following describes the transformation from $$f(x) = 3^x to$$ $$f(x) = 3$$^{x+2}$$ + 1$$?

Accepted Answer

Shift left 2 units and up 1 unit

Question 6

Given the function $$f(x) = (4/3)^x$$, is it exponential growth or decay?

Accepted Answer

Exponential growth

Question 7

Expand $$\ln\left(\frac{2x\sqrt{x^2$+1}}{x+3}\right)$$ using logarithm properties.

Accepted Answer

$$\ln 2 + \ln x + \frac{1}{2} \ln(x^2$+1) - \ln(x+3)$$

Question 8

A population of herbivores is modeled by $$P(t) = 600e$$^{0.14t}$$. After how many years will the population reach 3000$?

Accepted Answer

$$t = \frac{\ln 5}{0.14}$$

Question 9

Solve for $$x$$: $$\log_3$(x-5) + \log_3$(x+3) = 2$$

Accepted Answer

$$x = 8$$

Question 10

Which of the following is the domain of $$f(x) = \log_3$ x$$?

Accepted Answer

$$(0, \infty)$$

Question 11

Given $$a(x) = -2x$$ and $$b(x) = 3x^2$, what is a$$ \circ b(4)$$?

Accepted Answer

$$-96$$

Question 12

Which of the following is the correct simplification of $$\log_8$ 8^y$$?

Accepted Answer

$$y$$

Question 13

If $$f(x) = 2^x - 2 + 5$$, what is the range of $$f(x)$$?

Accepted Answer

$$(3, \infty)$$

Question 14

Which of the following is the correct expansion of $$\log_2$\left(\frac{x^2$-4}{x+5}\right)$$?

Accepted Answer

$$\log_2$(x^2-4$$) - \$$log_2(x+5$$)$

Question 15

Given $$b(x) = 3x^2$ and c(x$$) = \sqrt{x-5}$$, what is b$$ \circ c(9)$$?

Accepted Answer

$$48$$

Question 16

Determine if $$F(x) = 2x - 1$$ and $$G(x) = -2x + 1$$ are inverses. Explain your answer.

Accepted Answer

No, because $$F(G(x)) 
eq x$$ and $$G(F(x)) 
eq x$$

Question 17

If $$\ln e^3$ is simplified, what is the result?

Accepted Answer

$$3$$

Question 18

Which of the following is the correct simplification of $$(16x^6$$)^{\frac{1}$${2}}$?

Accepted Answer

$$4x^3$$

Question 19

A radioactive material decays according to $$A = A_0$ e$$^{-0.00693x}$$. If A_0$ = 500$$ pounds and $$A = 406$$ pounds, how much time $$x (in $$years) will need to pass?

Accepted Answer

$$x = \frac{\ln(406/500)}{-0.00693}$$

Precalculus Exponents, Logarithms, Exponential/Logarithmic Equations, and Function Operations Study Guide

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