Introduction to Inverse Functions

The inverse is not a function

A function's inverse may not always be a function. The function (blue) $f(x)=x^2$, includes the points $(-1,1)$ and $(1,1)$. Therefore, the inverse would include the points: $(1,-1)$ and $(1,1)$ which the input value repeats, and therefore is not a function. For $f(x)=\sqrt{x}$ to be a function, it must be defined as positive.

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

Julien Coyne CC BY-SA 3.0.

Introduction to Inverse Functions

The inverse is not a function

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