g(x) = (-173x + 15) / 3. Find g^-1(g(5)) and g(g^-1(-12)).

Question

Instructions: Find equations for f^-1(x) for the following. 

Answer 1

This is kind of a trick question.  If a function g takes a value A as an input and gives the value B as an output, then the very definition of g^-1 is that it takes the value B as an input and gives the value A as an output.  So by definition 

 

g^-1(g(x)) = x for all x in the domain of g, and 

g(g^-1(x)) = x for all x in the domain of g^-1 

 

So g^-1(g(5)) = 5  and  g(g^-1(-12)) = -12  

 

You could figure out what g^-1 is and go thru all the calculations (and you'll get some good practice doing arithmetic if you do), but you don't have to do that to solve this problem.