Question

How do you find the inverse of `f(x) = x^2 +x`?

Answer 1

`f^-1(x)=-1/2+-sqrt(x+1/4)`

Explanation:

To find an inverse, switch x and y (or f(x)).

For simplicity I will rewrite f(x) as y...
`y=x^2+x`
switch...
`x=y^2+y`
now solve for y
It looks like we need to complete the square...
`x+1/4=y^2+y+1/4`
`x+1/4=(y+1/2)^2`
`+-sqrt(x+1/4)=y+1/2` Don't forget the `+-`!
`-1/2+-sqrt(x+1/4)=y` Don't forget the `+-`!