What is the inverse of f(x)= 1/(sqrt(x^2+x-6)) ?

The inverse of f(x)= 1/(sqrt(x^2+x-6)) is (-x+sqrt(25x^2+4))/(2x),-(x+sqrt(25x^2+4))/(2x)

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inverse of f(x)= 1/(sqrt(x^2+x-6))

inverse

f (x) = \frac{1}{x ^{2} + x - 6}

\frac{- x + 25 x ^{2} + 4}{2 x}, - \frac{x + 25 x ^{2} + 4}{2 x}

Solution steps

y = \frac{1}{x ^{2} + x - 6}

Replace

x

with

y

x = \frac{1}{y ^{2} + y - 6}

Solve for

y, x = \frac{1}{y ^{2} + y - 6}

\frac{- x + 25 x ^{2} + 4}{2 x}, - \frac{x + 25 x ^{2} + 4}{2 x}

What is the inverse of f(x)= 1/(sqrt(x^2+x-6)) ?
The inverse of f(x)= 1/(sqrt(x^2+x-6)) is (-x+sqrt(25x^2+4))/(2x),-(x+sqrt(25x^2+4))/(2x)