Question 1

Given the function $$f(x) = 2x + 1$$ and $$g(x) = x^2$ - 3$$, what is the value of $$(f \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = 2(2^2$ - 3) + 1 = 2(1) + 1 = 3$$

Question 2

Which of the following intervals describes where the function $$h(x) is $$decreasing, given the graph below?

Accepted Answer

$$(2, 4)$$

Question 3

If $$f(x) = 3x - 2$$ and $$g(x) = x + 4$$, what is $$(f + g)(x)$$?

Accepted Answer

$$3x - 2 + x + 4 = 4x + 2$$

Question 4

Given $$f(x) = x^2$ and g(x) = x - 1$, find (f - g)(3$$)$$.

Accepted Answer

$$f(3) - g(3) = 9 - 2 = 7$$

Question 5

A company’s monthly cost to produce $$x$$ units is $$C(x) = 2500 + 1.25x. If $$each unit sells for $$3.00$$, write the revenue function $$R(x)$$ and the profit function $$P(x).$$

Accepted Answer

$$R(x) = 3x$$, $$P(x) = 3x - (2500 + 1.25x)$$

Question 6

Given $$f(x) = x^2$ + 1$$ and $$g(x) = 2x$$, find $$(f \cdot g)(-1).$$

Accepted Answer

$$f(-1) \cdot g(-1) = (1 + 1) \cdot (-2) = 2 \cdot (-2) = -4$$

Question 7

If $$f(x) = 2x + 3$$ and $$g(x) = x - 1$$, what is the domain of $$\left(\frac{f}{g}\right)(x)$$?

Accepted Answer

$$x 
eq 1$$

Question 8

Given $$f(x) = 3x + 4$$, find the inverse function $$f^{-1}(x$$)$$.

Accepted Answer

$$f^{-1}(x$$) = \frac{x - 4}{3}$$

Question 9

Which of the following graphs represents a one-to-one function?

Accepted Answer

A graph that passes both the vertical and horizontal line tests

Question 10

Suppose $$f(x) = x^2$ and g(x) = x + 1$. What is (f$$ \circ g)(-2)$$?

Accepted Answer

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

Question 11

Given the piecewise function $$f(x) = \begin{cases} 2x + 3 & x \u003c -2 \ -x + 2 & x \geq -2 \end{cases}$$, what is $$f(-3)$$?

Accepted Answer

$$2(-3) + 3 = -6 + 3 = -3$$

Question 12

If $$f(x) = \frac{2x+1}{3x-4}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$x 
eq \frac{4}{3}$$

Question 13

Given $$f(x) = x^2$ and g(x) = 2x + 1$, find g(f(2$$))$$.

Accepted Answer

$$g(f(2)) = g(4) = 2 \cdot 4 + 1 = 9$$

Question 14

Which of the following statements is TRUE about the inverse of a function?

Accepted Answer

The inverse function reverses the roles of the input and output.

Question 15

Given the table below for $$f(x)$$:

$$x$$: $$0, 1, 2, 3$$

$$f(x)$$: $$2, 4, 8, 16$$

What is $$f^{-1}(8$$)$$?

Accepted Answer

$$2$$

Question 16

If $$f(x) = x^3$ and g(x$$) = \sqrt[3]{x}$$, what is (f$$ \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = f(g(x)) = (\sqrt[3]{x})^3$ = x$$

Question 17

A function $$f is $$invertible if and only if:

Accepted Answer

$$f is $$one-to-one (passes the horizontal line test)

Question 18

Given $$f(x) = 2x - 5$$, find $$x$$ such that $$f(x) = 7.$$

Accepted Answer

$$x = 6$$

Question 19

Suppose $$f(x) is $$increasing on $$(-\infty, 2)$$ and decreasing on $$(2, \infty). $$What is the nature of $$x = 2$$?

Accepted Answer

$$x = 2 is a $$local maximum

Question 20

If $$f(x) = x^2$ and g(x) = x + 1$, which of the following is the correct expression for (f + g)(x$$)$$?

Accepted Answer

$$x^2 + x + 1$

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