# What is the inverse function of f(x)=x^2?

What is the inverse function of $f\left(x\right)={x}^{2}$?
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einfachmoipf
Hence $f\left(x\right)={x}^{2}⇒y={x}^{2}⇒\sqrt{y}=\sqrt{{x}^{2}}⇒\sqrt{y}=|x|⇒x=±\sqrt{y}$

Wendy Boykin
Explanation:
If we try to solve $y={x}^{2}$ for x we do not get a single value.That means we do not get a function.
We get $x=±\sqrt{y}$
In order to be invertible a function must be one-to-one.
That means that we must have:
for every ${x}_{1}\ne {x}_{2}$, we have $f\left(-1\right)=f\left(1\right)$ (for example), so there is no inverse function.