What is the value of g(2) if f(x) = x^3 – x and g(f(1)) = 1 and g(2) = 1?

To solve for g(2), we first need to unpack the relationships presented in the question. We know that:

• f(x) is defined as f(x) = x³ – x.
• g(f(1)) = 1.
• g(2) = 1.

Let’s first calculate f(1):

f(1) = 13 - 1 = 1 - 1 = 0.

Now we have f(1) = 0, thus:

g(f(1)) = g(0) = 1.

This means g(0) = 1. Next, we look at the other part of the question where it states g(2) = 1. Since we already know that g(0) = 1, this doesn’t directly affect our calculation, but we can see that the function g gives 1 for at least two different inputs: 0 and 2.

Hence, the value of g(2) is given in the question itself, which is:

g(2) = 1.

Therefore, we conclude that the value of g(2) is:

1.