Please help with the answer and explanation?

We know that g(x) = \frac{3}{x^2+2x}

We have to find g^-1(x)  or inverse of g(x)

Inverse of g(x) can be determined by equating g(x) to y, and determining the value of x in terms of y

g(x) = y = \frac{3}{x^2+2x}

⇒ y × (x² + 2x) = 3

⇒ yx² + 2xy = 3

⇒ yx² + 2yx - 3 = 0

Determining the roots of x using:

x = OR x = , where a is coefficient of x², b is coefficient of x, and c is the constant

⇒ x = OR x =

⇒ x = OR x =

Hence, g^-1(x) = OR x =