How do you find the inverse of f(x) = x^2 + x and is it a function?

1 Answer
May 16, 2018

inverse relation is g(x) = \frac{-1\pm \sqrt{1+4x)}{2}

Explanation:

let y = f(x) = x^2 + x
solve for x in terms of y using the quadratic formula:
x^2+x-y = 0,
use quadratic formula x = \frac{-b\pm \sqrt{b^2-4ac}}{2a}

sub in a=1, b=1, c = -y
x = \frac{-1\pm \sqrt{1^2-4(-y)}}{2}
x = \frac{-1\pm \sqrt{1+4y)}{2}

Therefore the inverse relation is y = \frac{-1\pm \sqrt{1+4x)}{2}

Note that this is a relation and not a function because for each value of y, there are two values of x and functions cannot be multivalued