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

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

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

inverse

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

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

Solution steps

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

Replace

y

with

x

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

Solve for

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

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

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

f (x) = (x + 1)^{2} - 1

x^{2} + 3

f (x) = x^{2} + 5 x + 6

f (x) = 1.1011 E 13

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