What is the inverse of f(x)=log_{4}((x-1)^2) ?

The inverse of f(x)=log_{4}((x-1)^2) is sqrt(4^x)+1,-sqrt(4^x)+1

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inverse of f(x)=log_{4}((x-1)^2)

inverse

f (x) = lo g_{4} ((x - 1)^{2})

4^{x} + 1, - 4^{x} + 1

Solution steps

y = lo g_{4} ((x - 1)^{2})

Replace

x

with

y

x = lo g_{4} ((y - 1)^{2})

Solve for

y, x = lo g_{4} ((y - 1)^{2})

4^{x} + 1, - 4^{x} + 1

What is the inverse of f(x)=log_{4}((x-1)^2) ?
The inverse of f(x)=log_{4}((x-1)^2) is sqrt(4^x)+1,-sqrt(4^x)+1