What is the inverse of f(x)=-0.5x^2+1.5x ?

The inverse of f(x)=-0.5x^2+1.5x is -(-3+sqrt(-8x+9))/2 ,(sqrt(-8x+9)+3)/2

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inverse of f(x)=-0.5x^2+1.5x

inverse

f (x) = - 0.5 x^{2} + 1.5 x

- \frac{- 3 + - 8 x + 9}{2}, \frac{- 8 x + 9 + 3}{2}

Solution steps

y = - 0.5 x^{2} + 1.5 x

Replace

x

with

y

x = - 0.5 y^{2} + 1.5 y

Solve for

y, x = - 0.5 y^{2} + 1.5 y

- \frac{- 3 + - 8 x + 9}{2}, \frac{- 8 x + 9 + 3}{2}

100 (4 - 4 y)

f (x) = x + 4, x \geq 0

f (x) = 1 + e^{x}

6 x + 2

- x - 2

What is the inverse of f(x)=-0.5x^2+1.5x ?
The inverse of f(x)=-0.5x^2+1.5x is -(-3+sqrt(-8x+9))/2 ,(sqrt(-8x+9)+3)/2