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

The inverse of 2/(sqrt(-x^2+4x+5)) is -(-2x+sqrt(9x^2-4))/x ,(2x+sqrt(9x^2-4))/x

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

inverse

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

- \frac{- 2 x + 9 x ^{2} - 4}{x}, \frac{2 x + 9 x ^{2} - 4}{x}

Solution steps

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

Replace

x

with

y

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

Solve for

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

- \frac{- 2 x + 9 x ^{2} - 4}{x}, \frac{2 x + 9 x ^{2} - 4}{x}

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

f (x) = 3 + 2 x - 9

\frac{1}{1 + x ^{2}}

f (x) = \frac{8}{4 + x}

What is the inverse of 2/(sqrt(-x^2+4x+5)) ?
The inverse of 2/(sqrt(-x^2+4x+5)) is -(-2x+sqrt(9x^2-4))/x ,(2x+sqrt(9x^2-4))/x