$$f(-x) = f(x)$$ \text{ for all } x \text{ in the domain}$

Question 1

Which of the following best describes the domain of the function $$f(x) = \sqrt{x-4}$$?

Accepted Answer

$$x \geq 4$$

Question 2

Given $$f(x) = x^2$ - 16$$ and $$g(x) = \sqrt{x+5}$$, what is the domain of the composite function $$(g \circ f)(x)$$?

Accepted Answer

Question 3

If $$f(x) = -3x^4$ + 7x^2$ - 1$$, which of the following best describes the symmetry of $$f(x)$$?

Accepted Answer

Even function; symmetric about the $$y-$$axis

Question 4

Given the piecewise function $$h(x) = \begin{cases} 2x+1, & x  3 \end{cases}$$, what is the value of $$h(4)$$?

Accepted Answer

$$16$$

Question 5

Which of the following statements is true about the function $$f(x) = x^3$ - x$$?

Accepted Answer

It is an odd function because $$f(-x) = -f(x)$$

Question 6

Suppose $$f(x) = \sqrt{x+5}$$ and $$g(x) = x^2$. What is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$x \geq 0$$

Question 7

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

Accepted Answer

$$x \in \mathbb{R}$$

Question 8

A function is called even if:

Accepted Answer

$$f(-x) = f(x)$$ 	ext{ for all } x 	ext{ in the domain}$

Question 9

Given the graph of $$k(x) as $$shown, which of the following is the correct range of $$k(x)$$?

Accepted Answer

$$[-2, 4]$$

Question 10

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

Accepted Answer

$$9$$

Question 11

Given $$f(x) = \sqrt{x-4}$$, for which value of $$x is$$ $$f(x)$$ defined?

Accepted Answer

$$x = 4$$

Question 12

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is (g$$ \circ f)(-2)$$?

Accepted Answer

$$2$$

Question 13

Which of the following is the correct definition of the domain of a composite function $$(f \circ g)(x)$$?

Accepted Answer

The set of all $$x$$ such that $$x is in $$the domain of $$g$$ and $$g(x) is in $$the domain of $$f$$

Question 14

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

Accepted Answer

$$10$$

Question 15

If $$f(x) = x^2$ and g(x$$) = \sqrt{x}$$, what is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$x \geq 0$$

Question 16

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

Accepted Answer

$$7$$

Question 17

Suppose $$f(x) = x^2$ and g(x) = x + 1$. What is (f - g)(3$$)$$?

Accepted Answer

$$5$$

Question 18

Given $$f(x) = x^2$ and g(x) = x + 1$, what is (f$$ \cdot g)(2)$$?

Accepted Answer

$$12$$

Question 19

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

Accepted Answer

$$\dfrac{4}{3}$$

Precalculus Study Notes: Functions, Domains, Ranges, and Composition

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