Root function

Definition

A root function is a function that involves the extraction of roots, typically square roots or cube roots, of variables. It is commonly represented as $f(x) = \sqrt[n]{x}$ where $n$ is a positive integer.

5 Must Know Facts For Your Next Test

1. The domain of the square root function $f(x) = \sqrt{x}$ is $x \geq 0$ because you cannot take the square root of a negative number in real numbers.
2. The graph of a square root function $f(x) = \sqrt{x}$ starts at the origin (0,0) and increases gradually.
3. For odd root functions like $f(x) = \sqrt[3]{x}$, the domain includes all real numbers because you can take an odd root of any real number.
4. Root functions are non-linear; their graphs are curves rather than straight lines.
5. The inverse function of a square root function $f(x) = \sqrt{x}$ is the squaring function $g(x) = x^2$.

Review Questions

• What is the domain of the square root function $f(x) = \sqrt{x}$?
• How does the graph of the cube root function $f(x) = \sqrt[3]{x}$ differ from that of the square root function?
• What is the inverse function of $f(x) = \sqrt{x}$?

Related terms

Square Root: A number which produces a specified quantity when multiplied by itself. For example, $\sqrt{4} = 2$.

Cube Root: $\sqrt[3]{x}$ represents a value that when cubed gives x. For example, $\sqrt[3]{8} = 2$.

Inverse Function: A function that reverses another function: if the original function maps x to y, then its inverse maps y back to x.