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

The inverse of f(x)=(1+x)/(sqrt(x-1)) is (-2+x^2+xsqrt(x^2-8))/2 ,(-2+x^2-xsqrt(x^2-8))/2

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inverse of f(x)=(1+x)/(sqrt(x-1))

inverse

f (x) = \frac{1 + x}{x - 1}

\frac{- 2 + x ^{2} + x x ^{2} - 8}{2}, \frac{- 2 + x ^{2} - x x ^{2} - 8}{2}

Solution steps

y = \frac{1 + x}{x - 1}

Replace

x

with

y

x = \frac{1 + y}{y - 1}

Solve for

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

\frac{- 2 + x ^{2} + x x ^{2} - 8}{2}, \frac{- 2 + x ^{2} - x x ^{2} - 8}{2}

What is the inverse of f(x)=(1+x)/(sqrt(x-1)) ?
The inverse of f(x)=(1+x)/(sqrt(x-1)) is (-2+x^2+xsqrt(x^2-8))/2 ,(-2+x^2-xsqrt(x^2-8))/2