.
Given g(x)= -12x-5
Find g^-1(-5)
~~~~~~~~~~~~~~~~
To answer the question, you do not need to express the function g^(-1)(x) explicitly: it is an excessive unnecessary work.
What you really need is to solve equation g(x) = -5 and find x.
It is just enough and can be done in couple of lines.
To answer the question, you need to solve equation g(x) = 5, which is
12x - 5 = -5 and implies 12x = 0, x = 0.
ANSWER. x= 0.
Solved.