The original function and its inverse function must satisfy the following formula (condition)
f∧-1(f(x)) =x
We will check
f(x)=2x+4 and g(x)= (x-4)/2
f(g(x))= f((x-4)/2) = 2*((x-4)/2) +4= x-4+4= x it is correct
g(f(x))= g(2x+4) = (2*(x-4)/2 +4)= x-4+4= x it is correct
Or we can find inverse function of the f(x)
f∧-1(f(x))=x => f∧-1(2x+4)=x
=> We introduce new variable t and get
2x+4=t => 2x= t-4 => x= (t-4)/2
When we replace that in the inverse function we get
f∧-1 (t)= (t-4)/2
when we declare t with x we finally get
f∧-1 (x) = (x-4)/2 which is the same as g(x)= (x-4)/2
We have proved that the following functions are inverses of each other.
Good luck!!!