If f(x) = x^2 for each x in (-inf, inf), then f(f(f(x))) / f(x) is equal to _______. A. f(x) B. (f(x))^2 C. (f(x))^3 D. (f(x))^8

GATE 2020 · General Aptitude · Functions · medium

Answer: (f(x))^3 (Option C)

1. Compute f(f(x)): Apply f to x^2: square it to get x^4.
2. Compute f(f(f(x))): Apply f to x^4: square it to get x^8.
3. Divide by f(x) and express in terms of f(x): x^8 / x^2 = x^(8-2) = x^6 = (x^2)^3.