For x ≠ 2, define f(x) = (x+3)/(x−2). Other than x = 2, for what value of x is f(f(x)) undefined?

f(f(x)) is undefined wherever f(x) itself equals 2 (since that makes the outer denominator zero), besides where x=2 makes the inner f(x) undefined. Solve f(x) = 2: (x+3)/(x−2) = 2 → x+3 = 2x−4 → x = 7. So f(f(x)) is undefined at x = 2 (inner undefined) and at x = 7 (outer denominator zero). Simplifying f(f(x)) algebraically gives (4x−3)/(7−x), whose denominator vanishes exactly at x = 7, confirming the answer.