Final answer:
The functions f(x) = 3x - 1 and g(x) = x/13 are not inverses of each other, as the composition f(g(x)) and g(f(x)) does not equal the input x.
Step-by-step explanation:
To determine if the two functions f(x) = 3x - 1 and g(x) = x/13 are inverses of each other, we need to verify if composing one with the other returns the input variable x. To do this, we calculate f(g(x)) and g(f(x)).
The composition f(g(x)) is f(x/13) which equals 3(x/13) - 1 = x/13 - 1. As we can see, f(g(x)) does not simplify to x, hence this shows that f(x) and g(x) are not inverses of each other.
Secondly, computing g(f(x)) gives us g(3x - 1) which equals (3x - 1)/13. Once again, this does not simplify to x, confirming that the functions are not inverses.
Therefore, the answer to whether f(x) = 3x - 1 and g(x) = x/13 are inverses of each other is false.