What is the inverse of f(x)=(1+x)x ?

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

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inverse of f(x)=(1+x)x

inverse

f (x) = (1 + x) x

\frac{- 1 + 1 + 4 x}{2}, \frac{- 1 - 1 + 4 x}{2}

Solution steps

y = (1 + x) x

Replace

x

with

y

x = (1 + y) y

Solve for

y, x = (1 + y) y

\frac{- 1 + 1 + 4 x}{2}, \frac{- 1 - 1 + 4 x}{2}

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

f (4) = 9 x - 13

x^{2} - x - 5

x^{2} - x - 3

f (x) = \frac{x + 3}{x + 13}

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