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

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

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

inverse

f (x) = x \cdot (x + 1)

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

Solution steps

y = x (x + 1)

Replace

x

with

y

x = y (y + 1)

Solve for

y, x = y \cdot (y + 1)

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

16 y^{2} - 9 x^{2} = 144

f (x) = \frac{9}{3 - 10 x}

\frac{1}{5} x^{5} + x^{4} + x^{3}

f (x) = \frac{x ^{2} + 5}{3 x ^{2} - 14 x - 5}

f (x) = (x - 2)^{2} (x - 7)

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