What is the inverse of f(x)=(8x)/(x^2+81) ?

The inverse of f(x)=(8x)/(x^2+81) is (4+sqrt(-81x^2+16))/x ,(4-sqrt(-81x^2+16))/x

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inverse of f(x)=(8x)/(x^2+81)

inverse

f (x) = \frac{8 x}{x ^{2} + 81}

\frac{4 + - 81 x ^{2} + 16}{x}, \frac{4 - - 81 x ^{2} + 16}{x}

Solution steps

y = \frac{8 x}{x ^{2} + 81}

Replace

x

with

y

x = \frac{8 y}{y ^{2} + 81}

Solve for

y, x = \frac{8 y}{y ^{2} + 81}

\frac{4 + - 81 x ^{2} + 16}{x}, \frac{4 - - 81 x ^{2} + 16}{x}

What is the inverse of f(x)=(8x)/(x^2+81) ?
The inverse of f(x)=(8x)/(x^2+81) is (4+sqrt(-81x^2+16))/x ,(4-sqrt(-81x^2+16))/x