Q: Given $$f(x) = \dfrac{2x + 4}{3x - 1}$$, what is the inverse function $$f^{-1}(x$$)$$?

$$f^{-1}(x$$) = \dfrac{x + 4}{3x - 2}$$, x$$ \neq \dfrac{2}{3}$$

Question 1

Which of the following is the correct solution to the quadratic equation $$2x(x + 2) = 7$$?

Accepted Answer

$$x = \dfrac{-2 \pm 3\sqrt{2}}{2}$$

Question 2

Simplify $$(3 - 2i)(4 + 5i)$$ and write your answer in the form $$a + bi.$$

Accepted Answer

$$22 + 7i$$

Question 3

Which of the following is the correct simplification of the compound rational expression $$\dfrac{\dfrac{x-2}{x+2} - 1}{\dfrac{x-2}{x+2} + 1}$$?

Accepted Answer

$$-\dfrac{2}{x}$$

Question 4

Solve the absolute value inequality $$9|1 + 8n| - 3 \leq 78$$ for $$n.$$

Accepted Answer

$$-\dfrac{5}{4} \leq n \leq 1$$

Question 5

Find the domain of the function $$f(x) = \dfrac{\sqrt{x} - 2}{x^2$ + x - 6}.$$

Accepted Answer

$$(2, \infty)$$

Question 6

Given $$f(x) = x^2$ - x on$$ $$[-2, -1]$$, what is the average rate of change on this interval?

Accepted Answer

$$-4$$

Question 7

Which of the following functions is odd?

Accepted Answer

$$f(x) = x^3$ - x$$

Question 8

Let $$f(x) = \dfrac{4x - 3}{x + 1}$$ and $$g(x) = \dfrac{x + 4}{x - 3}. $$What is $$(f \circ g)(x)$$?

Accepted Answer

$$\dfrac{x + 25}{2x + 1}$$

Question 9

A ball is thrown upward from a platform 5 feet above the ground. Its height in feet after $$t$$ seconds is $$h(t) = -16t^2$ + 40t + 5. $$What is the maximum height of the ball, and when does it occur?

Accepted Answer

30 ft at $$t = 1.25 s$$

Question 10

The concentration of a medication in a patient's bloodstream is modeled by $$C(t) = 12t e$$^{-0.35t}$$ for 0$$ \leq t \leq 24$$. At what time does the absolute maximum concentration occur (rounded to the nearest tenth)?

Accepted Answer

$$t \approx 2.9$$ hours

Question 11

Given $$f(x) = \sqrt{x - 1}$$ and $$g(x) = x^2$ + 3$$, what is the domain of $$(g \circ f)(x)$$?

Accepted Answer

$$[1, \infty)$$

Question 12

Which of the following statements about the function $$f(x) = |x| - 4 is $$true?

Accepted Answer

It is even and symmetric about the $$y-$$axis.

Question 13

Given $$f(x) = \dfrac{2x + 4}{3x - 1}$$, what is the inverse function $$f^{-1}(x$$)$$?

Accepted Answer

$$f^{-1}(x$$) = \dfrac{x + 4}{3x - 2}$$, x$$ 
eq \dfrac{2}{3}$$

Question 14

A firework is launched and its height is modeled by $$h(t) = -0.2t^3$ + 2.4t^2$ + 3t. $$What does the $$y-$$intercept of this function represent in context?

Accepted Answer

The initial height of the firework at launch ($$t = 0)$$

Question 15

Which of the following best describes the concavity of the function $$f(x) = 2x^6$ - x^2$?

Accepted Answer

Concave up for all $$x$$ except near $$x = 0$$

Question 16

Given $$f(x) = x^2$ + 3x$$, find the simplified difference quotient $$\dfrac{f(x + h) - f(x)}{h}.$$

Accepted Answer

$$2x + 3 + h$$

Question 17

Which of the following is the correct domain for $$f(x) = \dfrac{x + 5}{\sqrt{x^2$ - 9}}$$?

Accepted Answer

$$(-\infty, -3) \cup (3, \infty)$$

Question 18

If $$f(x) = x^3$ - 2x$$, what is the average rate of change on the interval $$[0, 3]$$?

Accepted Answer

$$7$$

Question 19

Which of the following is the correct simplification of $$-4i^3$$ + $$7i^2 - 2i$$ + $$i^4$$?

Accepted Answer

$$-6 + 2i$$

Precalculus Unit 1 Review: Step-by-Step Study Guidance

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