Suppose f(x) = (5 – x)3 and, g(x) = a + x2, and f(g(x)) = (1 – x2)3. What is the value of a?

Substitute g(x) = a + x² into f: f(g(x)) = (5 − a − x²)³. For this to equal (1 − x²)³, the constant terms inside the cubes must match, so 5 − a = 1 and a = 4; the correct choice is a = 4.

AI-written and checked against the verified answer.