What is the inverse of f(x)=(2x)/(x^2-4) ?

The inverse of f(x)=(2x)/(x^2-4) is (1+sqrt(4x^2+1))/x ,(1-sqrt(4x^2+1))/x

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inverse of f(x)=(2x)/(x^2-4)

inverse

f (x) = \frac{2 x}{x ^{2} - 4}

\frac{1 + 4 x ^{2} + 1}{x}, \frac{1 - 4 x ^{2} + 1}{x}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{1 + 4 x ^{2} + 1}{x}, \frac{1 - 4 x ^{2} + 1}{x}

\frac{4}{x} + 9

f (x) = \frac{2 x}{4 - x}

sin (0)

f (x) = \frac{6}{x + 2}

f (x) = \frac{x}{4} - 2

What is the inverse of f(x)=(2x)/(x^2-4) ?
The inverse of f(x)=(2x)/(x^2-4) is (1+sqrt(4x^2+1))/x ,(1-sqrt(4x^2+1))/x