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

$$(f + g)(2) = f(2) + g(2) = (3 \times 2 - 4) + (2^2$) = 2 + 4 = 6$$

Question 1

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

Accepted Answer

$$f(g(2)) = f(0) = 2(0) + 1 = 1$$

Question 2

Which of the following intervals describes where the function $$h(x) is $$decreasing, given the graph below passes through $$(0, 4)$$, $$(2, 0)$$, and $$(4, 2)$$ and is a 'V' shape opening upwards?

Accepted Answer

$$(-\infty, 2)$$

Question 3

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

Accepted Answer

$$(f + g)(2) = f(2) + g(2) = (3 	imes 2 - 4) + (2^2$) = 2 + 4 = 6$$

Question 4

A company’s monthly cost to manufacture hats is $$C(x) = 2300 + 1.25x$$, where $$x is $$the number of hats. If each hat sells for $$11$$, what is the profit function $$P(x)$$?

Accepted Answer

$$P(x) = 11x - (2300 + 1.25x) = 9.75x - 2300$$

Question 5

Given $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2$$, find $$(f \div g)(2).$$

Accepted Answer

$$(f \div g)(2) = \dfrac{f(2)}{g(2)} = \dfrac{2^2$ - 4}{2 + 2} = \dfrac{0}{4} = 0$$

Question 6

Which of the following is the correct inverse of $$f(x) = \dfrac{2x + 1}{3x - 4}$$?

Accepted Answer

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

Question 7

Given the graph of $$f(x)$$ passes the vertical line test but fails the horizontal line test, which of the following is true?

Accepted Answer

$$f(x) is a $$function but not one-to-one, so it does not have an inverse that is a function.

Question 8

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

Accepted Answer

$$(f \circ g)(-2) = f(g(-2)) = f(-2 + 1) = f(-1) = (-1)^2$ = 1$$

Question 9

Suppose $$h(x) is $$defined by the table below:

$$x$$ | $$h(x)$$
---|---
0 | 2
1 | 5
2 | 10
3 | 17

What is the value of $$h(2) - h(0)$$?

Accepted Answer

$$h(2) - h(0) = 10 - 2 = 8$$

Question 10

Given $$f(x) = x^2$ - 4$$ and $$g(x) = x + 2$$, for which value of $$x is$$ $$(g \div f)(x)$$ undefined?

Accepted Answer

$$x = 2$$ and $$x = -2$$, because $$f(2) = 0$$ and $$f(-2) = 0$$

Question 11

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

Accepted Answer

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

Question 12

Which of the following best describes the domain of the function $$f(x) = \dfrac{1}{x-3}$$?

Accepted Answer

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

Question 13

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

Accepted Answer

$$(f \cdot g)(-1) = f(-1) \cdot g(-1) = 1 \cdot 1 = 1$$

Question 14

If $$f(x) is $$invertible and $$f(3) = 7$$, what is $$f^{-1}(7$$)$$?

Accepted Answer

$$3$$

Question 15

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

Accepted Answer

The inverse of a function $$f$$ undoes the action of $$f$$; that is, $$f^{-1}(f(x)) = x$ for all x$ in the domain of f$.

Question 16

Given the piecewise function $$f(x) = \begin{cases} 2x + 3 & x \u003c -2 \ x^2$ - 5 & x \geq -2 \end{cases}$$, what is $$f(-3)$$?

Accepted Answer

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

Question 17

Suppose $$f(x) is a $$function whose graph passes both the vertical and horizontal line tests. Which of the following is true?

Accepted Answer

$$f(x) is $$one-to-one and has an inverse that is also a function.

Question 18

Given $$f(x) = x^2$ and g(x) = x + 2$, what is (g$$ \circ f)(-2)$$?

Accepted Answer

$$(g \circ f)(-2) = g(f(-2)) = g(4) = 4 + 2 = 6$$

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