Question 1

What is the domain of the function $$f(x) = \sqrt{7 - x}$$?

Accepted Answer

$$(-\infty, 7]$$

Question 2

What is the range of the function $$f(x) = \sqrt{7 - x}$$?

Accepted Answer

$$[0, \infty)$$

Question 3

What is the domain of the function $$g(y) = \frac{1}{y-2}$$?

Accepted Answer

$$(-\infty, 2) \cup (2, \infty)$$

Question 4

Let $$f(x) = e^x + 2$$ and $$g(x) = x + 3. $$What is $$g(f(x))$$?

Accepted Answer

$$e^x + 5$$

Question 5

Let $$f(x) = e^x + 2$$ and $$g(x) = x + 3. $$What is $$f(g(x))$$?

Accepted Answer

$$e^{x+3} + 2$

Question 6

Given $$f(x) = e^x + 2$$ and $$g(x) = x + 3$$, express $$f \circ g(x) in $$the form $$ae^{bx} + c$.

Accepted Answer

$$e^{x+3} + 2$

Question 7

For $$f(x) = e^x + 2x$$, compute the difference quotient $$\frac{f(x+h) - f(x)}{h}$$ and simplify.

Accepted Answer

$$\frac{e$$^{x+h}$$ - e^x}{h} + 2$$

Question 8

For $$f(x) = x^2$, compute the difference quotient $$\frac{f(x+h) - f(x)}{h}$$ and simplify.

Accepted Answer

$$2x + h$$

Question 9

Which of the following best describes the range of $$g(y) = \frac{1}{y-2}$$?

Accepted Answer

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

Question 10

If $$f(x) = \sqrt{7-x}$$, what is the value of $$f(3)$$?

Accepted Answer

$$2$$

Question 11

Suppose $$f(x) = e^x + 2$$ and $$g(x) = x + 3. $$What is $$f(g(0))$$?

Accepted Answer

$$e^3 + 2$

Question 12

Which of the following is NOT in the domain of $$f(x) = \sqrt{7-x}$$?

Accepted Answer

$$x = 8$$

Question 13

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

Accepted Answer

$$(x+3)^2$$

Question 14

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

Accepted Answer

$$x^2 + 3$

Question 15

For $$f(x) = x^2$, what is the simplified form of the difference quotient $$\frac{f(x+h) - f(x)}{h}$$?

Accepted Answer

$$2x + h$$

Section 1.1: Review of Functions – Study Notes and Practice Problems

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