Question:

The functions f and g are defined by:

$\displaystyle f : x \mapsto 3x + 2$███$\displaystyle x \in \Re$

$\displaystyle g : x \mapsto \frac{6}{2x + 3}$███$\displaystyle x \neq 1.5$

(i)...

(ii)...

(iii) Express each of $\displaystyle f^{-1}(x)$ and $\displaystyle g^{-1}(x)$ in terms of $\displaystyle x$, and solve the equation $\displaystyle f^{-1}(x) = g^{-1}(x)$

Attempt:

$\displaystyle f(x) = 3x + 2$

$\displaystyle y = 3x + 2$

$\displaystyle y - 2 = 3x$

$\displaystyle \frac{y - 2}{3} = x$

$\displaystyle f^{-1}(x) = \frac{x - 2}{3}$

$\displaystyle g(x) = \frac{6}{2x + 3}$

I don't know how to get the inverse of g(x)