Restricting Domains to Find Inverses

Failure of horizontal line test

Graph of a parabola with the equation $y=x^2$, the U-Shaped curve opening up. This function fails the horizontal line test, and therefore does not have an inverse. The inverse equation, $y=\sqrt{x}$ (other graph) only includes the positive input values of the parabola's domain. However, if we restrict the domain to be $x>0$, then we find that it passes the horizontal line test and will match the inverse function.

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"Original figure by Julien Coyne. Licensed CC BY-SA 4.0."

Julien Coyne CC BY-SA 3.0.

Restricting Domains to Find Inverses

Failure of horizontal line test

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