Question 1

Which of the following values must be excluded from the domain of the function $$f(x) = \frac{1}{x^2$ - 49}$$?

Accepted Answer

$$x = 7$$ and $$x = -7$$

Question 2

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

Accepted Answer

All real numbers

Question 3

If $$f(x) = \sqrt{x-2}$$ and $$g(x) = x+1$$, what is the domain of the composite function $$f(g(x))$$?

Accepted Answer

$$x \geq 1$$

Question 4

Let $$f(x) = \frac{1}{x}$$ and $$g(x) = x^2$ - 4. $$What is the domain of the function $$f(g(x))$$?

Accepted Answer

$$x 
eq 2$$ and $$x 
eq -2$$

Question 5

Which of the following correctly describes the domain of the quotient $$\frac{f(x)}{g(x)} if$$ $$f(x)$$ and $$g(x)$$ are both defined for all real numbers?

Accepted Answer

All real numbers except where $$g(x) = 0$$

Question 6

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

Accepted Answer

$$x \geq 0$$

Question 7

Suppose $$f(x) = \sqrt{9 - x}$$ and $$g(x) = x + 2. $$What is the domain of $$f(g(x))$$?

Accepted Answer

$$x \leq 7$$

Question 8

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

Accepted Answer

$$x 
eq 0$$

Question 9

Which of the following is the correct expression for the composite function $$f(g(x)) if$$ $$f(x) = 2x + 1$$ and $$g(x) = x^2$?

Accepted Answer

$$2x^2 + 1$

Question 10

A medication’s effectiveness $$E(t) is $$modeled by $$E(t) = \frac{100}{t^2$ + 1}$$, where $$t is $$time in hours. What is the domain of $$E(t)$$?

Accepted Answer

All real numbers

Question 11

Let $$f(x) = \sqrt{x}$$ and $$g(x) = 5 - x^2$. What is the domain of the composite function f(g(x$$))$$?

Accepted Answer

$$-\sqrt{5} \leq x \leq \sqrt{5}$$

Question 12

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

Accepted Answer

$$x 
eq 3$$

Question 13

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

Accepted Answer

$$x \geq -1$$

Question 14

If $$f(x) = \frac{1}{x}$$ and $$g(x) = \sqrt{x}$$, what is the domain of $$f(g(x))$$?

Accepted Answer

$$x \u003e 0$$

Question 15

A company’s profit $$P(x) is $$modeled by $$P(x) = 500x - x^2$, where x$ is the number of units sold. What is the domain of P(x$$)$$ if only non-negative units can be sold?

Accepted Answer

$$x \geq 0$$

Combinations and Compositions of Functions: Domains and Operations

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