What is the inverse of f(x)= 3/4 x^2+5x-3/5 ?

The inverse of f(x)= 3/4 x^2+5x-3/5 is (-100+sqrt(1200x+10720))/(30),(-100-sqrt(1200x+10720))/(30)

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inverse of f(x)= 3/4 x^2+5x-3/5

inverse

f (x) = \frac{3}{4} x^{2} + 5 x - \frac{3}{5}

\frac{- 100 + 1200 x + 10720}{30}, \frac{- 100 - 1200 x + 10720}{30}

Solution steps

y = \frac{3}{4} x^{2} + 5 x - \frac{3}{5}

Replace

x

with

y

x = \frac{3}{4} y^{2} + 5 y - \frac{3}{5}

Solve for

y, x = \frac{3}{4} y^{2} + 5 y - \frac{3}{5}

\frac{- 100 + 1200 x + 10720}{30}, \frac{- 100 - 1200 x + 10720}{30}

What is the inverse of f(x)= 3/4 x^2+5x-3/5 ?
The inverse of f(x)= 3/4 x^2+5x-3/5 is (-100+sqrt(1200x+10720))/(30),(-100-sqrt(1200x+10720))/(30)