What is the inverse of f(x)=(4x)/(sqrt(5x^2+4)) ?

The inverse of f(x)=(4x)/(sqrt(5x^2+4)) is sqrt(-(4x^2)/(5x^2-16)),-sqrt(-(4x^2)/(5x^2-16))

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inverse of f(x)=(4x)/(sqrt(5x^2+4))

inverse

f (x) = \frac{4 x}{5 x ^{2} + 4}

- \frac{4 x ^{2}}{5 x ^{2} - 16}, - - \frac{4 x ^{2}}{5 x ^{2} - 16}

Solution steps

y = \frac{4 x}{5 x ^{2} + 4}

Replace

x

with

y

x = \frac{4 y}{5 y ^{2} + 4}

Solve for

y, x = \frac{4 y}{5 y ^{2} + 4}

- \frac{4 x ^{2}}{5 x ^{2} - 16}, - - \frac{4 x ^{2}}{5 x ^{2} - 16}

y = 2 x^{2} - 4 x + 1

\frac{5 x + 1}{2 x - 3}

\frac{x + 2}{x + 7}

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

\frac{x + 2}{x + 8}

What is the inverse of f(x)=(4x)/(sqrt(5x^2+4)) ?
The inverse of f(x)=(4x)/(sqrt(5x^2+4)) is sqrt(-(4x^2)/(5x^2-16)),-sqrt(-(4x^2)/(5x^2-16))