What is the inverse of f(x)=-1/2 x^2+4x-3 ?

The inverse of f(x)=-1/2 x^2+4x-3 is -(-8+sqrt(-8x+40))/2 ,-(-8-sqrt(-8x+40))/2

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inverse of f(x)=-1/2 x^2+4x-3

inverse

f (x) = - \frac{1}{2} x^{2} + 4 x - 3

- \frac{- 8 + - 8 x + 40}{2}, - \frac{- 8 - - 8 x + 40}{2}

Solution steps

y = - \frac{1}{2} x^{2} + 4 x - 3

Replace

x

with

y

x = - \frac{1}{2} y^{2} + 4 y - 3

Solve for

y, x = - \frac{1}{2} y^{2} + 4 y - 3

- \frac{- 8 + - 8 x + 40}{2}, - \frac{- 8 - - 8 x + 40}{2}

f (x) = 14 x + 5

x^{2} + x + 2

x^{2} + x - 6

y = x^{2} - 4

What is the inverse of f(x)=-1/2 x^2+4x-3 ?
The inverse of f(x)=-1/2 x^2+4x-3 is -(-8+sqrt(-8x+40))/2 ,-(-8-sqrt(-8x+40))/2