To verify that g(x) is the inverse of f(x), we need to show that f(g(x)) = x and g(f(x)) = x.
First, let’s calculate f(g(x)). We know that g(x) = 13x, so we substitute this into f(x):
f(g(x)) = f(13x) = 3(13x) = 39x.
Now, we need to find g(f(x)). We know that f(x) = 3x, so we substitute this into g(x):
g(f(x)) = g(3x) = 13(3x) = 39x.
Since both f(g(x)) and g(f(x)) produce the result 39x instead of x, this shows that g(x) is not the inverse of f(x). For g(x) to be the inverse of f(x), we would need to find expressions that simplify to just x when composed together. In this case, neither verifies that g(x) is the inverse of f(x).