A Value of the Inverse

You do not need the whole inverse rule to find one value of it. ${g}^{-1}\left(23\right)$ asks: which input does g send to 23? So write $g\left(x\right) = 23$ and solve for x.

Take $g\left(x\right) = 3x+2$. Using the rule turns the question into $3x+2 = 23$, so $3x = 21$ and x is 7. That means ${g}^{-1}\left(23\right) = 7$. Check forwards: g(7) is 21 + 2, which is 23.

This works because the inverse swaps inputs and outputs: g sends 7 to 23 exactly when its inverse sends 23 to 7. Solving one equation is quicker than finding the full inverse rule and then evaluating it.