Final answer:
To verify the inverse relationship between f(x) = 3x and g(x) = 1/3x, we show that f(g(x)) = x and g(f(x)) = x, which confirms that each function undoes the other's effect, characteristic of inverse functions.
Step-by-step explanation:
To verify that g(x) is the inverse of f(x), we need to show that applying g after f will return the original input value. Specifically, with f(x) = 3x and g(x) = 1/3x, we confirm this by showing that composing the two functions yields the identity function, which is to say that f(g(x)) = x and g(f(x)) = x.
Let's apply g to f and vice versa:
- f(g(x)) = f(1/3x) = 3(1/3x) = x
- g(f(x)) = g(3x) = 1/3(3x) = x
Thus, each function 'undoes' the effect of the other, fulfilling the primary characteristic of inverse functions, which means g(x) is indeed the inverse of f(x).