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

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

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inverse of f(x)=(2x)/(1+x^2)

inverse

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

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

Solution steps

y = \frac{2 x}{1 + x ^{2}}

Replace

x

with

y

x = \frac{2 y}{1 + y ^{2}}

Solve for

y, x = \frac{2 y}{1 + y ^{2}}

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

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