What is the inverse of f(x)=(2/x-3)/(4/(x^2)-9) ?

The inverse of f(x)=(2/x-3)/(4/(x^2)-9) is -(2x)/(3x-1)

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inverse of f(x)=(2/x-3)/(4/(x^2)-9)

inverse

f (x) = \frac{\frac{2}{x} - 3}{\frac{4}{x ^{2}} - 9}

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

Solution steps

y = \frac{\frac{2}{x} - 3}{\frac{4}{x ^{2}} - 9}

Replace

x

with

y

x = \frac{\frac{2}{y} - 3}{\frac{4}{y ^{2}} - 9}

Solve for

y, x = \frac{\frac{2}{y} - 3}{\frac{4}{y ^{2}} - 9}

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

\frac{1}{4} x^{3} - 2

ln (3 + x) - 2

f (x) = (x^{2} - 4)^{\frac{1}{2}}

f (x) = (x - 3) + 7

f (x) = (x - 3) + 2

What is the inverse of f(x)=(2/x-3)/(4/(x^2)-9) ?
The inverse of f(x)=(2/x-3)/(4/(x^2)-9) is -(2x)/(3x-1)