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

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Answer 1 · 2015-10-14T17:25:59

#f^-1(x)= sqrt(x+9)+3#

First you equate #f(x)# to another variable, say #f(x)=y#.

But before that, complete the square for #f(x)#.

#:. x^2-6x+3^2-3^2=(x-3)^2-9#

Now,
#y=(x-3)^2-9#
#(x-3)^2=y+9#
#(x-3)=sqrt(y+9)#
#x=sqrt(y+9)+3#

Now swap back the x for the variable y.

So the inverse for #f(x)# is
#f^-1(x)= sqrt(x+9)+3#