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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

\frac{( x ^{2} + 21 )}{9}

f (x) = 3 - 5 - x

\frac{2 x - 7}{9 x + 4}

f (x) = (5 - x)^{3}

f (x) = (\frac{( 7 - 3 x )}{( 2 x - 3 )})

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