Final answer:
To prove that g(x) is the inverse of f(x), we need to show that when we compose the functions f(g(x)) and g(f(x)), we get the identity function f(x) = x.
Step-by-step explanation:
To prove that g(x) is the inverse of f(x), we need to show that when we compose the functions f(g(x)) and g(f(x)), we get the identity function f(x) = x. Let's start by finding f(g(x)).
We have f(x) = 6y + 1 and g(x) = 1/6x - 1/6. Substituting g(x) into f(x) gives us f(g(x)) = 6*(1/6x - 1/6) + 1 = x + (6/6 - 1/6) = x.
Next, let's find g(f(x)). We have f(x) = 6y + 1, so substituting f(x) into g(x) gives us g(f(x)) = 1/6*(6y + 1) - 1/6 = y + 1/6 - 1/6 = y.
Since f(g(x)) = x and g(f(x)) = y, we have proven that g(x) is the inverse of f(x).