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

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

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

inverse

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

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

Solution steps

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

Replace

x

with

y

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

Solve for

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

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

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