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

The inverse of f(x)=-4/3 x^2+8/3 x-1/3 is -(-8+sqrt(-48x+48))/8 ,-(-8-sqrt(-48x+48))/8

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inverse of f(x)=-4/3 x^2+8/3 x-1/3

inverse

f (x) = - \frac{4}{3} x^{2} + \frac{8}{3} x - \frac{1}{3}

- \frac{- 8 + - 48 x + 48}{8}, - \frac{- 8 - - 48 x + 48}{8}

Solution steps

y = - \frac{4}{3} x^{2} + \frac{8}{3} x - \frac{1}{3}

Replace

x

with

y

x = - \frac{4}{3} y^{2} + \frac{8}{3} y - \frac{1}{3}

Solve for

y, x = - \frac{4}{3} y^{2} + \frac{8}{3} y - \frac{1}{3}

- \frac{- 8 + - 48 x + 48}{8}, - \frac{- 8 - - 48 x + 48}{8}

f (x) = 0.627226 x - 5.83079

f (x) = \frac{9 x + 10}{4 x - 5}

f (x) = 1 + x

4 - x + 8

4 - x + 1

What is the inverse of f(x)=-4/3 x^2+8/3 x-1/3 ?
The inverse of f(x)=-4/3 x^2+8/3 x-1/3 is -(-8+sqrt(-48x+48))/8 ,-(-8-sqrt(-48x+48))/8