To figure out if the functions f(x) and g(x) are inverse functions of each other, we will need to verify two properties:
1. f(g(x)) = x for all x in the domain
2. g(f(x)) = x for all x in the domain
Let's start with the first property.
We know f(x)=x+3, and g(x)=x-3. If we substitute g(x) into the function f(x), we get f(g(x)) = ((x-3)+3). We can simplify this to f(g(x)) = x. So, the first property is satisfied.
Now, let's verify the second property.
We know g(f(x))=(x+3)-3=x. So, the function g(f(x)) = x also holds true. Therefore, the second property is also satisfied.
In conclusion, since both the properties hold true, we can confidently say that the function f(x) is the inverse of g(x) and vice versa.