Learn How to Invert a Function with Mathematica for y = x^2

[kent davidge]

Suppose I have $y = x^2$. By inverse, I mean $x = \pm \sqrt y$. How can I get Mathematica to do that?

 

[Dale]

Solve[y==x^2,x]

 

[Mark44]

Suppose I have $y = x^2$. By inverse, I mean $x = \pm \sqrt y$. How can I get Mathematica to do that?

Technically speaking, $y = x^2$ doesn't have an inverse that is itself a function. For a function f to have an inverse, f must be one-to-one. Your example function fails this test because for each number x in the domain that maps to $x^2$, -x also maps to the same value.

 

[Dale]

Technically speaking, $y = x^2$ doesn't have an inverse that is itself a function. For a function f to have an inverse, f must be one-to-one. Your example function fails this test because for each number x in the domain that maps to $x^2$, -x also maps to the same value.

Solve finds and reports both.

 

[Mark44]

Solve finds and reports both.

Right. I checked with wolframalpha, which is sort of the online version of Mathematica.