Practice Domain in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

The domain of a function is the complete set of allowable input values for which the function produces a defined, valid output.

The domain is the list of valid "questions" you can ask the function — values outside the domain produce undefined or meaningless answers.

Showing a random 20 of 50 problems.

Example 1

easy

Find the domain of

f(x) = 3x - 5

Example 2

easy

Find the domain of

f(x) = \dfrac{3}{x^2 + 1}

Example 3

hard

Find the domain of

f(x) = \sqrt{x^2 - 5x + 6}

Example 4

hard

For what values of

k

does

f(x) = \sqrt{x^2 + kx + 1}

have domain all reals?

Example 5

easy

Find the domain of

f(x)=\sqrt{x}+\frac{1}{x-1}

Example 6

challenge

Find the domain of

f(x)=\sqrt{\frac{x-1}{x+2}}

Example 7

easy

Find the domain of

f(x) = \dfrac{1}{(x+1)(x-2)}

Example 8

easy

Find the domain of

f(x)=\frac{5}{x}

Example 9

medium

Find the domain of

f(x)=\log_2(2x-6)

Example 10

medium

Find the domain of

f(x) = \log(x^2 - 9)

Example 11

medium

Find the domain of

f(x) = \dfrac{1}{\sqrt{x - 4}}

Example 12

easy

Find the domain of

f(x)=2x+7

Example 13

medium

Find the domain of

f(x)=\frac{x-1}{x^2-x}

Example 14

easy

Find the domain of

f(x)=x^2-4x+1

Example 15

medium

Find the domain of

f(x) = \sqrt{x} + \sqrt{5 - x}

Example 16

medium

Find the domain of

h(x) = \frac{\sqrt{x + 1}}{x - 5}

Example 17

challenge

Find the domain of

f(x)=\frac{\sqrt{x+3}}{\sqrt{5-x}}

Example 18

medium

Find the domain of

f(x)=\log(x-1)+\log(7-x)

Example 19

easy

Find the domain of

f(x) = \sqrt[3]{x - 1}

Example 20

medium

Find the domain of

f(x) = \sqrt{16 - x^2}

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Related Concepts

Function Range Restricted Domain