key term - Inverse of a radical function

Definition

The inverse of a radical function is a function that reverses the operation of the original radical function, effectively swapping the roles of inputs and outputs. It typically involves solving for the variable inside the radical and expressing it in terms of the output variable.

5 Must Know Facts For Your Next Test

1. The domain of a radical function must be restricted to ensure its inverse is also a function.
2. The inverse of $f(x) = \sqrt{x}$ is $f^{-1}(x) = x^2$ for $x \geq 0$.
3. If you have $f(x) = \sqrt[n]{x}$, its inverse will generally be $f^{-1}(x) = x^n$, with appropriate domain restrictions.
4. To find the inverse, you solve the equation $y = \sqrt{f(x)}$ for $x$ in terms of $y$.
5. The graph of a radical function and its inverse are reflections across the line $y=x$.

Review Questions

Related terms

Radical Function:

A function that involves roots, such as square roots or cube roots.

Domain:

The set of all possible input values (x-values) for which a given function is defined.

Reflection Across y=x: A transformation producing a mirror image of a graph across the line $y=x$.