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

The inverse of f(x)=sqrt(3x^2+5x-2) is (-5+sqrt(12x^2+49))/6 ,(-5-sqrt(12x^2+49))/6

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

inverse

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

\frac{- 5 + 12 x ^{2} + 49}{6}, \frac{- 5 - 12 x ^{2} + 49}{6}

Solution steps

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

Replace

x

with

y

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

Solve for

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

\frac{- 5 + 12 x ^{2} + 49}{6}, \frac{- 5 - 12 x ^{2} + 49}{6}

\frac{x - 1}{1 + 4 x}

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

f (x) = (x - 1)^{3} - 3

f (x) = \frac{6}{8 + x}

f (x) = 4 x - 13

What is the inverse of f(x)=sqrt(3x^2+5x-2) ?
The inverse of f(x)=sqrt(3x^2+5x-2) is (-5+sqrt(12x^2+49))/6 ,(-5-sqrt(12x^2+49))/6