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

The inverse of f(x)=2x+3-1/3 x^2 is -(-6+sqrt(-12x+72))/2 ,-(-6-sqrt(-12x+72))/2

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

inverse

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

- \frac{- 6 + - 12 x + 72}{2}, - \frac{- 6 - - 12 x + 72}{2}

Solution steps

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

Replace

x

with

y

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

Solve for

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

- \frac{- 6 + - 12 x + 72}{2}, - \frac{- 6 - - 12 x + 72}{2}

\frac{4}{x - 3}

x^{2} + 7

(0, 240), (227, 0)

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

sin (π + 4 x)

What is the inverse of f(x)=2x+3-1/3 x^2 ?
The inverse of f(x)=2x+3-1/3 x^2 is -(-6+sqrt(-12x+72))/2 ,-(-6-sqrt(-12x+72))/2