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

$$x \u003e 0$$ and $$\sqrt{x} \neq 2$$

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

$$x \neq \sqrt{2}$$,\ x \neq -\sqrt{2}$

Question 1

Given the functions $$f(x) = x^2$ + 3x - 10$$ and $$g(x) = x - 2$$, what is $$f(g(x))$$?

Accepted Answer

$$(x-2)^2 + 3(x-2) - 10$

Question 2

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

Accepted Answer

$$(x+4)^2 - 3$

Question 3

Given $$f(x) = \sqrt{x+4}$$ and $$g(x) = (x-2)^2$ - 4$$, what is the domain of $$(f \circ g)(x)$$?

Accepted Answer

$$(x-2)^2 - 4$$ \geq -4$$

Question 4

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

Accepted Answer

$$4$$

Question 5

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

Accepted Answer

$$x \u003e 0$$ and $$\sqrt{x} 
eq 2$$

Question 6

Which of the following correctly expresses $$h(x) = \sqrt{x-2} as a $$composition of two functions $$f$$ and $$g$$ such that $$h(x) = (f \circ g)(x)$$?

Accepted Answer

$$f(x) = \sqrt{x},\ g(x) = x-2$$

Question 7

Given $$f(x) = x^2$ + 3x - 10$$ and $$g(x) = x - 2$$, what is $$(g \circ f)(x)$$?

Accepted Answer

$$x^2 + 3x - 10 - 2$

Question 8

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

Accepted Answer

$$7$$

Question 9

Given $$f(x) = \frac{1}{x^2$ - 3x - 10}$$, which of the following is a valid decomposition $$f(x) = (f_1$ \circ g_1$)(x)$$?

Accepted Answer

$$f_1(x$$) = \frac{1}{x},\ $$g_1(x$$) = $$x^2 - 3x - 10$

Question 10

Suppose $$f(x) = x^2$ and g(x$$) = \sqrt{x-8}$$. What is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$x \geq 8$$

Question 11

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

Accepted Answer

$$\sqrt{x^2$ + 2}$$

Question 12

If $$f(x) = x + 1$$ and $$g(x) = \sqrt{x}$$, what is $$(g \circ f)(x)$$?

Accepted Answer

$$\sqrt{x+1}$$

Question 13

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

Accepted Answer

$$x 
eq \sqrt{2}$$,\ x 
eq -\sqrt{2}$

Question 14

If $$f(x) = x^2$ + 3x - 10$$ and $$g(x) = x - 2$$, what is $$(f \circ g)(3)$$?

Accepted Answer

$$-2$$

Question 15

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

Accepted Answer

$$25$$

Question 16

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

Accepted Answer

$$\sqrt{x^2$ + 1}$$

Question 17

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

Accepted Answer

$$(x+1)^2$$

Question 18

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

Accepted Answer

$$x 
eq 2,\ x 
eq -2$$

Question 19

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

Accepted Answer

$$x,\ x \geq 0$$

Question 20

Which of the following is a correct decomposition of $$h(x) = \frac{1}{x^2$ - 3x - 10} as$$ $$h(x) = (f \circ g)(x)$$?

Accepted Answer

$$f(x) = \frac{1}{x},\ g(x) = x^2$ - 3x - 10$$

Function Composition and Decomposition in College Algebra

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