Domain of Functions – Practice Questions with Answers

This page contains 20 practice questions on finding the domain of functions. The problems include polynomial, rational, square root, logarithmic, exponential, and absolute value functions. Complete answers are provided at the end of the page.

For interactive practice, visit: Finding the Domain of Functions


Questions

Question 1

Find the domain of

\[ f(x) = 2x + 7 \]

Question 2

Find the domain of

\[ g(x) = \frac{1}{-x + 8} \]

Question 3

Find the domain of

\[ h(x) = \frac{x - 6}{2x - 8} \]

Question 4

Find the domain of

\[ f(x) = \frac{5}{\sqrt{-x + 4}} \]

Question 5

Find the domain of

\[ h(x) = \frac{\sqrt{-x + 5}}{\sqrt{x - 3}} \]

Question 6

Find the domain of

\[ f(x) = \sqrt{|x| - 5} \]

Question 7

Find the domain of

\[ f(x) = \sqrt{|3x - 8| - 5} \]

Question 8

Find the domain of

\[ f(x) = \frac{3x - 6}{x^2 + 2x - 8} \]

Question 9

Find the domain of

\[ h(x) = \frac{3x - 6}{\sqrt{x^2 + 2x - 8}} \]

Question 10

Find the domain of

\[ g(x) = |2x - 4| \]

Question 11

Find the domain of

\[ h(x) = \ln(|2x - 9|) \]

Question 12

Find the domain of

\[ g(x) = \frac{1}{x^2 + 6} \]

Question 13

Find the domain of

\[ g(x) = \frac{1}{\sqrt{x^2 + 2x + 6}} \]

Question 14

Find the domain of

\[ h(x) = \frac{1}{\sqrt{| -x^2 - 9 |}} \]

Question 15

Find the domain of the function defined by the set of ordered pairs:

\[ g = \{(3,2),(5,9),(6,9),(11,0)\} \]

Question 16

Find the domain of

\[ g(x) = \frac{1}{2 - \sqrt{x + 2}} \]

Question 17

Find the domain of

\[ f(x) = e^{\ln(x)} \]

Question 18

Find the domain of

\[ f(x) = \frac{1}{\log(2x - 3)} \]

Question 19

Find the domain of

\[ g(x) = \ln(2x - 8) \]

Question 20

Find the domain of

\[ g(x) = \log(x^2 + 3x - 10) \]

Answers

\[ \begin{aligned} 1)&\; (-\infty,\infty) \\ 2)&\; (-\infty,8)\cup(8,\infty) \\ 3)&\; (-\infty,4)\cup(4,\infty) \\ 4)&\; (-\infty,4) \\ 5)&\; (3,5] \\ 6)&\; (-\infty,-5]\cup[5,\infty) \\ 7)&\; (-\infty,1]\cup\left[\frac{13}{3},\infty\right) \\ 8)&\; (-\infty,-4)\cup(-4,2)\cup(2,\infty) \\ 9)&\; (-\infty,-4)\cup(2,\infty) \\ 10)&\; (-\infty,\infty) \\ 11)&\; \left(-\infty,\frac{9}{2}\right)\cup\left(\frac{9}{2},\infty\right) \\ 12)&\; (-\infty,\infty) \\ 13)&\; (-\infty,\infty) \\ 14)&\; (-\infty,\infty) \\ 15)&\; \{3,5,6,11\} \\ 16)&\; [-2,2)\cup(2,\infty) \\ 17)&\; (0,\infty) \\ 18)&\; \left(\frac{3}{2},2\right)\cup(2,\infty) \\ 19)&\; (4,\infty) \\ 20)&\; (-\infty,-5)\cup(2,\infty) \end{aligned} \]

More References