What is the inverse of f(x)= 1/((x-1)^2) ?

The inverse of f(x)= 1/((x-1)^2) is sqrt(1/x)+1,-sqrt(1/x)+1

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inverse of f(x)= 1/((x-1)^2)

inverse

f (x) = \frac{1}{( x - 1 ) ^{2}}

\frac{1}{x} + 1, - \frac{1}{x} + 1

Solution steps

y = \frac{1}{( x - 1 ) ^{2}}

Replace

x

with

y

x = \frac{1}{( y - 1 ) ^{2}}

Solve for

y, x = \frac{1}{( y - 1 ) ^{2}}

\frac{1}{x} + 1, - \frac{1}{x} + 1

What is the inverse of f(x)= 1/((x-1)^2) ?
The inverse of f(x)= 1/((x-1)^2) is sqrt(1/x)+1,-sqrt(1/x)+1