Q: Joe invests $$750 in a $$savings account that compounds interest daily. He wants to double his money in 3 years. What annual interest rate $$r$$ does he need? (Use $$A = P(1+\frac{r}{365}$$)^{365t}$$)

$$r = 365\left[(2$$)^{1/3}$$ - 1\right] \times 100\%$$

Q: A laboratory has $$11.3 mg of Re-188$$, which has a half-life of $$16.9$$ hours. How much will remain after $$10$$ hours?

$$11.3 \times \left(\frac{1}{2}\$$right)^{10/16.9}$$ mg

Question 1

Given the functions $$f(x) = \frac{2x}{x-1}$$ and $$g(x) = \frac{x}{2}$$, what is the domain of $$f(g(x))$$?

Accepted Answer

$$x 
eq 2$$

Question 2

Which of the following is the inverse of the function $$F(x) = \frac{2x+1}{x}$$?

Accepted Answer

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

Question 3

Given the relation $$\{(-1,4), (1,4), (4,-7), (7,-8)\}$$, what is the range?

Accepted Answer

$$\{4, -7, -8\}$$

Question 4

Which transformation is applied to $$f(x) = |x| to $$obtain $$f(x) = |x| - 2$$?

Accepted Answer

Vertical shift down by 2 units

Question 5

What is the horizontal asymptote of the function $$f(x) = \frac{2x+1}{x}$$?

Accepted Answer

$$y = 2$$

Question 6

Find the domain of $$f(x) = \log_{2}(x^2$ - 9).$$

Accepted Answer

$$x  3$$

Question 7

Expand $$\log_{4}(x^2$y^7$$)$ as a sum of logarithms.

Accepted Answer

$$2\log$$_{4}$$x + 7\log$$_{4}$$y$$

Question 8

Simplify $$2\ln \sqrt{e}.$$

Accepted Answer

$$1$$

Question 9

Solve for $$x$$: $$27^{x-1}(3$$^{x}$$)^{2} = 81$.

Accepted Answer

$$x = 2$$

Question 10

If $$f(x) = \log_{2}(x+2) + 1$$, what is the vertical asymptote of $$f(x)$$?

Accepted Answer

$$x = -2$$

Question 11

A car loan has a maximum monthly payment of $$520, an interest rate of 4.9$$\%$$ for 5 years, compounded monthly. What is the maximum amount John can borrow? (Use P$$ = \frac{M}{\frac{i}{$$1-(1+i)^{-n}$$}}$$, where i$$ = \frac{r}{12}$$ and n = 60$)

Accepted Answer

$$P = \frac{520}{\frac{0.049/12}{1-(1+0.049/12$$)^{-60}$$}}$$

Question 12

Joe invests $$750 in a $$savings account that compounds interest daily. He wants to double his money in 3 years. What annual interest rate $$r$$ does he need? (Use $$A = P(1+\frac{r}{365}$$)^{365t}$$)

Accepted Answer

$$r = 365\left[(2$$)^{1/3}$$ - 1ight] 	imes 100\%$$

Question 13

A laboratory has $$11.3 mg of Re-188$$, which has a half-life of $$16.9$$ hours. How much will remain after $$10$$ hours?

Accepted Answer

$$11.3 	imes \left(\frac{1}{2}\$$right)^{10/16.9}$$ mg

Question 14

Which of the following relations is one-to-one?

Accepted Answer

$$\{(1,2), (2,3), (3,4)\}$$

Question 15

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

Accepted Answer

$$f(g(1)) = 2$$

Question 16

Which of the following is the correct simplification for $$\log$$_{10}$$18 - \log$$_{10}$$9$$?

Accepted Answer

$$\log$$_{10}$$2$$

Question 17

Solve for $$x$$: $$5^{2x} = 3$$ \cdot $$5^{x}.$$

Accepted Answer

$$x = 1$$

Question 18

Which of the following is the correct expression for $$\log_{3}(x^2$y^7$$)$ as a sum of logarithms?

Accepted Answer

$$2\log$$_{3}$$x + 7\log$$_{3}$$y$$

Question 19

If $$f(x) = \log_{2}(x^2$ - 9)$$, which of the following intervals is NOT in the domain?

Accepted Answer

$$(-3,3)$$

Precalculus Exam 4 Review: Functions, Logarithms, Exponentials, and Applications

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