What is the inverse of f(x)=(3x)/(5+x^2) ?

The inverse of f(x)=(3x)/(5+x^2) is (3+sqrt(9-20x^2))/(2x),(3-sqrt(9-20x^2))/(2x)

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inverse of f(x)=(3x)/(5+x^2)

inverse

f (x) = \frac{3 x}{5 + x ^{2}}

\frac{3 + 9 - 20 x ^{2}}{2 x}, \frac{3 - 9 - 20 x ^{2}}{2 x}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{3 + 9 - 20 x ^{2}}{2 x}, \frac{3 - 9 - 20 x ^{2}}{2 x}

y = 5 x + 6 x^{2}

f (x) = e^{8 x - 9}

f (x) = \frac{x - 2}{x + 3}

f (x) = e^{- 2 x^{2}}

- \frac{3}{2} cos (3 x - \frac{1}{2}) + 2

What is the inverse of f(x)=(3x)/(5+x^2) ?
The inverse of f(x)=(3x)/(5+x^2) is (3+sqrt(9-20x^2))/(2x),(3-sqrt(9-20x^2))/(2x)