$$\{x \mid x \neq 5, x \neq 3\}$$

Question 1

Given $$f(x) = x^2$ and g(x) = x + 4$, what is the value of (f$$ \circ g)(2)$$?

Accepted Answer

$$f(g(2)) = f(6) = 36$$

Question 2

Which of the following best describes the composite function $$(f \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = f(g(x))$$

Question 3

If $$f(x) = x^2$ and g(x) = x + 4$, what is the formula for (f$$ \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = (x + 4)^2$

Question 4

Given $$f(x) = \frac{x}{x-1}$$ and $$g(x) = \frac{2}{x-5}$$, what is the domain of $$f(x)$$?

Accepted Answer

$$\{x \mid x 
eq 1\}$$

Question 5

For $$f(x) = \frac{x}{x-1}$$ and $$g(x) = \frac{2}{x-5}$$, what is the domain of $$g(x)$$?

Accepted Answer

$$\{x \mid x 
eq 5\}$$

Question 6

Given $$f(x) = \frac{x}{x-1}$$ and $$g(x) = \frac{2}{x-5}$$, what is the formula for $$(f \circ g)(x)$$?

Accepted Answer

$$(f \circ g)(x) = \frac{\frac{2}{x-5}}{\frac{2}{x-5} - 1}$$

Question 7

What is the domain of $$(f \circ g)(x)$$ for $$f(x) = \frac{x}{x-1}$$ and $$g(x) = \frac{2}{x-5}$$?

Accepted Answer

$$\{x \mid x 
eq 5, x 
eq 3\}$$

Question 8

Why is $$x = 3$$ excluded from the domain of $$(f \circ g)(x)$$ when $$f(x) = \frac{x}{x-1}$$ and $$g(x) = \frac{2}{x-5}$$?

Accepted Answer

Because $$g(3) = \frac{2}{3-5} = -1$$ and $$f(-1) is $$undefined

Question 9

If $$f(x) = x^2$ and g(x) = x + 4$, which of the following is true about the range of f$$ \circ g$$?

Accepted Answer

The range of $$f \circ g is $$all real numbers greater than or equal to $$0$$

Question 10

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

Accepted Answer

It consists of all $$x in $$the domain of $$g$$ such that $$g(x) is in $$the domain of $$f$$

Question 11

Suppose $$f(x) = x^2$ and g(x) = x + 4$. What is (g$$ \circ f)(2)$$?

Accepted Answer

$$(g \circ f)(2) = g(f(2)) = g(4) = 8$$

Question 12

Given $$f(x) = x^2$ and g(x) = x + 4$, which of the following is the correct formula for (g$$ \circ f)(x)$$?

Accepted Answer

$$(g \circ f)(x) = x^2$ + 4$$

Question 13

If $$f(x) = \frac{x}{x-1}$$ and $$g(x) = \frac{2}{x-5}$$, what value(s) of $$x$$ make $$g(x) = -1$$?

Accepted Answer

$$x = 3$$

Question 14

Which of the following best describes the process of finding the domain of $$(f \circ g)(x)$$?

Accepted Answer

Find the domain of $$g$$, then restrict to values where $$g(x) is in $$the domain of $$f$$

Composite Functions and Their Domains

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