Skip to content

Physics Playground

Simulations How we teach Pricing

Language

Log in Start learning free

Loading…

Physics Playground

Built on open, peer-reviewed sources: OpenStax, The Feynman Lectures on Physics, HyperPhysics, NASA and NIST. See our sources.

Learn

Physics course
Math for Physics
Start with the math toolkit
Simulations
Glossary
Exercises
Past exams
Library
How we teach

Company

Pricing
Terms
Privacy
Contact

© 2026 Physics Playground. Made for the curious.Language

Exercises Polynomials and factoring

Example 5 from Precalculus, 3.8 Inverses and Radical Functions

Finding the Inverse of a Radical Function

Restrict the domain and then find the inverse of the function $f (x) = \sqrt{x - 4} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Note that the original function has range $f (x) \geq 0.$ Replace $f (x)$ with $y,$ then solve for $x .$

$\begin{matrix} y & = \sqrt{x - 4} & Replace f (x) with y . \\ x & = \sqrt{y - 4} & Interchange x and y . \\ x & = \sqrt{y - 4} & Square each side . \\ x^{2} & = y - 4 & Add 4 . \\ x^{2} + 4 & = y & Rename the function f^{- 1} (x) . \\ f^{- 1} (x) & = x^{2} + 4 \end{matrix}$
Recall that the domain of this function must be limited to the range of the original function.

$f^{- 1} (x) = x^{2} + 4, x \geq 0$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Restrict the domain and then find the inverse of the function $f (x) = \sqrt{2 x + 3} .$

How did it go?

PreviousIdentifying Horizontal and Slant Asymptotes

From Precalculus (1st edition) by OpenStax (Rice University), section 3.8, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.