Question

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

Answer 1

This function does not have an inverse.

Explanation:

We have that

`f(x)=(x^2-6x+9)-9=(x-3)^2-9`

hence `f(0)=f(6)` this function is not `1-1`

This function `f:R->R` does not have an inverse.

Answer 2

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^2-6y` for `y` using either Completing the Square or the Quadratics Formula:

`y^2-6y-x=0`

We have `a=1`, b=-6`and`c=-x#

`y = (-b +- sqrt(b^2-4ac))/2a`

`y = (-(-6) +- sqrt((-6)^2-4(1)(-x)))/(2(1))`

`y = (6+-sqrt(36+4x))/2`

`y = (6+-sqrt(4(9+4x)))/2`

`y = (6+- 2sqrt(9+4x))/2`

`y = 3 +- sqrt(9+x)`

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