Question 1

Which of the following describes the domain of the function $$f(x) = \frac{1}{x-3}$$?

Accepted Answer

$$(-\infty, 3) \cup (3, \infty)$$

Question 2

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

Accepted Answer

$$[0, \infty)$$

Question 3

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

Accepted Answer

$$[1, \infty)$$

Question 4

Let $$f(x) = x^2$ and g(x) = 2x + 3$. Which of the following is (f$$ \cdot g)(x)$$?

Accepted Answer

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

Question 5

A medical researcher models the concentration of a drug in the bloodstream as $$C(t) = \frac{100}{t+2}$$, where $$t is $$time in hours. What is the domain of $$C(t)$$?

Accepted Answer

$$(-2, \infty)$$

Question 6

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

Accepted Answer

$$[0, \infty)$$

Question 7

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

Accepted Answer

$$(1, \infty)$$

Question 8

Which of the following expresses $$h(x) = (3x + 2)^4$ as a composition of two functions f$ and g$?

Accepted Answer

$$f(x) = x^4$,\ g(x) = 3x + 2$$

Question 9

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

Accepted Answer

$$[-\sqrt{5}, \sqrt{5}]$$

Question 10

A biologist models the population of a bacteria colony as $$P(t) = 200e$$^{-0.5t}$$, where t$ is time in hours. If Q(t$$) = \ln(P(t))$$, what is the domain of Q(t$$)$$?

Accepted Answer

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

Question 11

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

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Question 12

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

Accepted Answer

$$(2, \infty)$$

Question 13

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

Accepted Answer

$$2x^2 + 1$

Question 14

A chemist mixes two solutions, where $$f(x) = x^2$ models the concentration of the first and g(x$$) = \sqrt{x}$$ the second. What is the domain of (f/g)(x$$)$$?

Accepted Answer

$$(0, \infty)$$

Question 15

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

Accepted Answer

$$(-\infty, 0) \cup (0, \infty)$$

Combinations of Functions and Composite Functions – Study Notes

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