# How do you find the inverse of f(x)=x^2-6x?

This function does not have an inverse.

#### Explanation:

We have that

$f \left(x\right) = \left({x}^{2} - 6 x + 9\right) - 9 = {\left(x - 3\right)}^{2} - 9$

hence $f \left(0\right) = f \left(6\right)$ this function is not $1 - 1$

This function $f : R \to R$ does not have an inverse.

Sep 10, 2015

The function is not one-to-one, so it does not have an inverse function.

#### Explanation:

The inverse relation may be found by solving

$x = {y}^{2} - 6 y$ for $y$ using either Completing the Square or the Quadratics Formula:

${y}^{2} - 6 y - x = 0$

We have $a = 1$, b=-6$\mathmr{and}$c=-x#

$y = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2} a$

$y = \frac{- \left(- 6\right) \pm \sqrt{{\left(- 6\right)}^{2} - 4 \left(1\right) \left(- x\right)}}{2 \left(1\right)}$

$y = \frac{6 \pm \sqrt{36 + 4 x}}{2}$

$y = \frac{6 \pm \sqrt{4 \left(9 + 4 x\right)}}{2}$

$y = \frac{6 \pm 2 \sqrt{9 + 4 x}}{2}$

$y = 3 \pm \sqrt{9 + x}$

As we can see $y$ is not a function of $x$. That is: the inverse relation is not a function.