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.