How do you find #f^-1(x)# given #f(x)=1/(x-1)^2#?

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How do you find #f^-1(x)# given #f(x)=1/(x-1)^2#?

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Answer 1 · 2016-11-05T06:10:42

THe answer is #=1/sqrtx+1#

Explanation:

Let #y=1/(x-1)^2#
So #(x-1)^2=1/y#
#x-1=1/sqrty#
#x=1/sqrty+1#
#:. f^-1(x)=1/sqrtx+1#
Verifications, we calculate
#f(f^-1(x))=f(1/sqrtx+1)=1/(1/sqrtx+1-1)^2=1/(1/sqrtx)^2#
#=1/(1/x)=x#

# :. #we have calculated #f^-1(x)#

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How do you find #f^-1(x)# given #f(x)=1/(x-1)^2#?

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