Question Detail
Question
If \( f(x) = x-1 \) and \( g(x) = x^2+1 \), then \( f(g(x)) = g(f(x)) \) when \( x = \)?
Correct Answer
Option B is the correct answer.
Detailed Explanation
( f(g(x)) = (x^2+1)-1 = x^2 ). ( g(f(x)) = (x-1)^2+1 = x^2 - 2x + 2 ). Setting them equal: ( x^2 = x^2 - 2x + 2 \implies 2x = 2 \implies x = 1 ).
Hint
Compose the functions and solve the resulting equation for \( x \).