How do you find the inverse of #g(x) = (x -5)^2#?

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Answer 1 · 2018-05-30T22:06:33

#g^-1(x) =5+sqrt(x )#

or

#g^-1(x) =5-sqrt(x )#

#g(x) = (x -5)^2#

#y = (x -5)^2#

Switch the #x# and #y#:

#x = (y -5)^2#

solve for #x#:

#+-sqrt(x )= sqrt((y -5)^2)#

#+-sqrt(x )= y -5#

#y=5+-sqrt(x )#

Now you have the problem that this inverse is not a function unless you restrict its range.

#g^-1(x) =5+sqrt(x )#

or

#g^-1(x) =5-sqrt(x )#