Find inverse functions for simple invertible functions, including rational examples.
Find an inverse function by swapping x and y and solving an exponential equation
Problem
Find \(f^{-1}(x)\) for \(f(x)~=~2^x\).
Big Picture
What this problem is really about
An exponential and a logarithm with the same base describe the same relationship from opposite directions. Swap the variables, then rewrite the exponential equation in logarithmic form so the unknown exponent becomes the output. The positive range of the original exponential becomes the input restriction of its inverse.
Inside Gozunta
Turn the preview into practice.
More than a preview
Gozunta lets you study this problem—and more than 10,000 others.
Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.
