What is the inverse of f(x)=-1/2 x^2-x+3/2 ?

The inverse of f(x)=-1/2 x^2-x+3/2 is -(2+sqrt(-8x+16))/2 ,-(2-sqrt(-8x+16))/2

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inverse of f(x)=-1/2 x^2-x+3/2

inverse

f (x) = - \frac{1}{2} x^{2} - x + \frac{3}{2}

- \frac{2 + - 8 x + 16}{2}, - \frac{2 - - 8 x + 16}{2}

Solution steps

y = - \frac{1}{2} x^{2} - x + \frac{3}{2}

Replace

x

with

y

x = - \frac{1}{2} y^{2} - y + \frac{3}{2}

Solve for

y, x = - \frac{1}{2} y^{2} - y + \frac{3}{2}

- \frac{2 + - 8 x + 16}{2}, - \frac{2 - - 8 x + 16}{2}

What is the inverse of f(x)=-1/2 x^2-x+3/2 ?
The inverse of f(x)=-1/2 x^2-x+3/2 is -(2+sqrt(-8x+16))/2 ,-(2-sqrt(-8x+16))/2