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

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

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

inverse

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

\frac{1 - x ^{2}}{x ^{2} + 1}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{1 - x ^{2}}{x ^{2} + 1}

f (x) = \frac{7 x}{x + 8}

f (x) = x^{4} - 1

y = \frac{x}{5} + 8

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