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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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

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

f (x) = e^{(x + 1)} + 1

f (x) = 7.7372 - 0.6974 x + 0.0134 x^{2}

1 - \frac{2 - 2}{3}

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