Q: A bank account earns $$10.25\%$$ interest compounded continuously. How much should you invest now to have $$100,000 in$$ $$18$$ years?

$$P = \frac{100000}{e$$^{0.1025 \times 18}$$}$$

Question 1

Which of the following statements correctly describes the relationship between a function $$f$$ and its inverse $$f^{-1}$$?

Accepted Answer

For all $$x in $$the domain of $$f$$, $$f(f^{-1}(x)) = x$ and f$$^{-1}$$(f(x)) = x$$

Question 2

Given the function $$f(x) = \sqrt{x+1}$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

Question 3

Suppose the temperature $$F in $$degrees Fahrenheit is given by $$F = \frac{9}{5}C + 32$$, where $$C is $$the temperature in degrees Centigrade. What is the inverse function that gives $$C in $$terms of $$F$$?

Accepted Answer

$$C = \frac{5}{9}(F - 32)$$

Question 4

Which of the following functions is self-inverse (i.e., its own inverse)?

Accepted Answer

$$g(x) = \frac{6}{x}$$

Question 5

A function $$f is $$one-to-one if and only if:

Accepted Answer

Each output value is produced by exactly one input value.

Question 6

Given the table below, what is $$f^{-1}(4$$)$$?

x$: -4$, -3$, 1$, 2$
f(x$$)$$: 3$, 1$, -3$, 4$

Accepted Answer

$$f^{-1}(4) = 2$

Question 7

Which graphical test can be used to determine if a function has an inverse?

Accepted Answer

Horizontal line test

Question 8

If $$f(x) = |x - 7|$$, does $$f$$ have an inverse over its entire domain?

Accepted Answer

No, because $$f is $$not one-to-one.

Question 9

Given the exponential function $$f(x) = 10 \cdot 2^x$$, what is the initial value and the base?

Accepted Answer

Initial value: $$10$$, Base: $$2$$

Question 10

A population of wild rabbits doubles every year. If there are initially $$100$$ rabbits, which equation models the population after $$x$$ years?

Accepted Answer

$$y = 100 \cdot 2^x$$

Question 11

Given the compound interest formula $$A = P \left(1 + \frac{r}{n}\$$right)^{nt}$$, what does n$ represent?

Accepted Answer

The number of times interest is compounded per year

Question 12

If $$P = 1500$$, $$r = 0.065$$, $$n = 4$$, and $$t = 5$$, what is the value of $$A$$ using the compound interest formula?

Accepted Answer

$$A = 1500 \left(1 + \frac{0.065}{4}\$$right)^{20}$$

Question 13

What is the value of $$e^{1.8} to $$three decimal places?

Accepted Answer

$$e^{1.8}$$ \approx 6.050$$

Question 14

If interest is compounded continuously, which formula should be used?

Accepted Answer

$$A = P e$$^{rt}$$

Question 15

A bank account earns $$10.25\%$$ interest compounded continuously. How much should you invest now to have $$100,000 in$$ $$18$$ years?

Accepted Answer

$$P = \frac{100000}{e$$^{0.1025 	imes 18}$$}$$

Question 16

Which of the following is the correct inverse of $$f(x) = 3x - 8$$?

Accepted Answer

$$f^{-1}(x$$) = \frac{x+8}{3}$$

Question 17

Which of the following statements about the graph of a function and its inverse is true?

Accepted Answer

The graph of the inverse is a reflection of the graph of the function across the line $$y = x$$

Question 18

If the horizontal asymptote of a function is $$y = -2$$, what does it become for the inverse function?

Accepted Answer

A vertical asymptote at $$x = -2$$

Question 19

Which of the following functions is NOT one-to-one?

Accepted Answer

$$h(x) = -\frac{1}{4}(x+1)^2$

Inverse Functions and Exponential Functions in College Algebra

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