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

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

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

inverse

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

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

\frac{3}{3 x + 12}

y = \frac{4 - x ^{2}}{x ^{2} - 1}

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

f (x) = 0.35 x^{2} - 0.7 x - 7

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

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