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Find the Domain of a Function - Questions

A set of 10 problems, on finding the domain of a function, with detailed solutions are presented. There are also more problems using the applet below.

You may want to work through a tutorial on finding the domain of a function Domain and range of functions.

Problem 1: Find the domain of the real-valued linear function $f$ given below.

$f(x) = x + 1$

Problem 2: Find the domain of the real-valued square root function $f$ given below.

$f(x) = \sqrt{2x}$

Problem 3: Find the domain of the real-valued rational function $f$ given below.

$f(x) = \frac{x - 1}{x - 3}$

Problem 4: Find the domain of the real-valued function $f$ given below.

$f(x) = \frac{\sqrt{-x + 1}}{x + 3}$

Problem 5: Find the domain of the real-valued cube root function $f$ given below.

$f(x) = \sqrt[3]{2x + 1}$

Problem 6: Find the domain of the real-valued logarithmic function $f$ given below.

$f(x) = \ln(x^2 - 9)$

Problem 7: Find the domain of the real-valued sine function $f$ given below.

$f(x) = 2\sin(x - 1)$

Problem 8: Find the domain of the real-valued exponential function $f$ given below.

$f(x) = e^{x - 4}$

Problem 9: Find the domain of the real-valued arcsine function $f$ given below.

$f(x) = \arcsin(x^2 - 1)$

Problem 10: Find the domain of the real-valued rational function $f$ given below.

$f(x) = \frac{1}{x^3 + x^2 -2x}$

References and Links

domain and range of basic functions.
Math Problems, Questions and Online Self Tests.
Step by Step Calculator to Find Domain of a Function