What is the inverse of f(x)=-x^2+5x-6 ?

The inverse of f(x)=-x^2+5x-6 is -(-5+sqrt(-4x+1))/2 ,-(-5-sqrt(-4x+1))/2

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inverse of f(x)=-x^2+5x-6

inverse

f (x) = - x^{2} + 5 x - 6

- \frac{- 5 + - 4 x + 1}{2}, - \frac{- 5 - - 4 x + 1}{2}

Solution steps

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

Replace

x

with

y

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

Solve for

y, x = - y^{2} + 5 y - 6

- \frac{- 5 + - 4 x + 1}{2}, - \frac{- 5 - - 4 x + 1}{2}

What is the inverse of f(x)=-x^2+5x-6 ?
The inverse of f(x)=-x^2+5x-6 is -(-5+sqrt(-4x+1))/2 ,-(-5-sqrt(-4x+1))/2