# 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.

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