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

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Answer 1 · 2015-09-10T20:45:36

This function does not have an inverse.

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 · 2015-09-10T21:00:58

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

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.

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