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

The inverse of f(x)=3x^2+5x-3 is (-5+sqrt(12x+61))/6 ,(-5-sqrt(12x+61))/6

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

inverse

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

\frac{- 5 + 12 x + 61}{6}, \frac{- 5 - 12 x + 61}{6}

Solution steps

y = 3 x^{2} + 5 x - 3

Replace

x

with

y

x = 3 y^{2} + 5 y - 3

Solve for

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

\frac{- 5 + 12 x + 61}{6}, \frac{- 5 - 12 x + 61}{6}

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

- 10 x

f (x) = \frac{e ^{x}}{9 + 4 e ^{x}}

f (x) = \frac{2 x + 7}{3 x - 8}

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

What is the inverse of f(x)=3x^2+5x-3 ?
The inverse of f(x)=3x^2+5x-3 is (-5+sqrt(12x+61))/6 ,(-5-sqrt(12x+61))/6