What is the inverse of f(x)=(2x)/(x^2+81) ?

The inverse of f(x)=(2x)/(x^2+81) is (1+sqrt(-81x^2+1))/x ,(1-sqrt(-81x^2+1))/x

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inverse of f(x)=(2x)/(x^2+81)

inverse

f (x) = \frac{2 x}{x ^{2} + 81}

\frac{1 + - 81 x ^{2} + 1}{x}, \frac{1 - - 81 x ^{2} + 1}{x}

Solution steps

y = \frac{2 x}{x ^{2} + 81}

Replace

x

with

y

x = \frac{2 y}{y ^{2} + 81}

Solve for

y, x = \frac{2 y}{y ^{2} + 81}

\frac{1 + - 81 x ^{2} + 1}{x}, \frac{1 - - 81 x ^{2} + 1}{x}

- lo g_{2} (3 x - 5)

y = 2^{- x}

y = \frac{2}{5} x + 3

f (x) = 3 x^{2} + 3

f (x) = \frac{25 - x ^{2}}{x - 5}

What is the inverse of f(x)=(2x)/(x^2+81) ?
The inverse of f(x)=(2x)/(x^2+81) is (1+sqrt(-81x^2+1))/x ,(1-sqrt(-81x^2+1))/x