Question

Given g(x)=3/x^2+2x find g^-1(x)

Answer 1

A

Explanation:

`g(x) = \frac{3}{{x}^(2) + 2x} \\ {x}^(2) + 2x - (3)/(g(x)) = 0 \\ x = (1)/(2) \Big( - 2 + \sqrt{12 + (12)/(g(x)) }\Big) \\ x = - 1 + \sqrt{1 \pm (3)/(g(x)) }`

Now replace $x$ by $g^{-1}(x)$ and $g(x)$ by $x$ and you have your answer.