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

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

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

inverse

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

1 - - 2 x + 1, - 2 x + 1 + 1

Solution steps

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

Replace

x

with

y

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

Solve for

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

1 - - 2 x + 1, - 2 x + 1 + 1

y = 6 x^{3} + 8 x^{2} - 5 x + 5

f (x) = \frac{x}{x ^{2} - ∣ x ∣}

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

2 x^{3} - 24 x

f (x) = - 7 x + 3

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