Question 1

Let $$f(x) = x^2$ - 6x + 8$$ and $$g(x) = x - 2. $$What is $$(fg)(x)$$?

Accepted Answer

$$x^3$$ - $$8x^2 + 20x - 16$

Question 2

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

Accepted Answer

$$[-2, 5]$$

Question 3

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

Accepted Answer

$$27$$

Question 4

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

Accepted Answer

$$(2x + 1)^2$ - 3$$

Question 5

Suppose $$f(x) = \frac{1}{x-3}$$ and $$g(x) = x^2$ + 1. $$What is the domain of $$(f \circ g)(x)$$?

Accepted Answer

$$(-\infty, \infty)$$

Question 6

A car dealer offers an 8% discount and a $$4000 rebate on a car with MSRP x$. If the rebate is applied first, what is the final price function?

Accepted Answer

$$0.92(x - 4000)$$

Question 7

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

Accepted Answer

$$[-2, 2]$$

Question 8

If $$h(x) = (2x^2$ + 1)^3$, which is a valid decomposition h(x) = f(g(x$$))$$?

Accepted Answer

$$f(x) = x^3$,\ g(x) = 2x^2$ + 1$$

Question 9

The area $$A of an $$oil spill is a function of time $$t in $$hours, with radius increasing at 2 miles/hour. What is $$A(t)$$?

Accepted Answer

$$A(t) = 4\pi t^2$

Question 10

If $$f(x) = \sqrt{x-2}$$ and $$g(x) = 18 - x^2$, what is the domain of (f$$ \circ g)(x)$$?

Accepted Answer

$$[2, 18]$$

Question 11

Let $$f(x) = x^2$ - 6x + 8$$ and $$g(x) = x - 2. $$What is $$(f-g)(x)$$?

Accepted Answer

$$x^2 - 7x + 10$

Question 12

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

Accepted Answer

$$[-2, 5)$$

Question 13

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

Accepted Answer

$$5$$

Question 14

A car dealer applies an 8% discount after a $$4000 rebate to MSRP x$. What is the final price function?

Accepted Answer

$$0.92(x - 4000)$$

Question 15

If $$f(x) = x^2$ - 6x + 8$$ and $$g(x) = x - 2$$, what is $$(f+g)(x)$$?

Accepted Answer

$$x^2 - 5x + 6$

Question 16

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

Accepted Answer

$$(-\infty, 5]$$

Question 17

If $$f(x) = x^2$ - 6x + 8$$ and $$g(x) = x - 2$$, what is $$(f/g)(x)$$?

Accepted Answer

$$\frac{x^2$ - 6x + 8}{x - 2}$$

Combining and Composing Functions in Precalculus

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