Answer: We can conclude that f(x) and g(x) are not inverses.
Explanation:
If we have two functions:
f(x) and g(x)
These functions are inverses if:
f( g(x) ) = x
g( f(x) ) = x
In this case, we have:
f(x) = 12*x - 12
g(x) = (1/12)*x - 1
Now we need to check the compositions:
f( g(x) ) = 12*g(x) - 12 = 12*( (1/12)*x - 1) - 12 = (x - 12) - 12 = x - 24
and:
g( f(x)) = (1/12)*f(x) - 1 = (1/12)*(12*x - 12) - 1 = 12*x/12 - 12/12 - 1 = x - 1 - 1 = x - 2
In both cases, we can see that:
f( g(x) ) ≠ x
and:
g( f(x) ) ≠ x
Then we can conclude that f(x) and g(x) are not inverses functions.