Question Statement:
Consider the following functions for non-zero positive integers, $p$ and $q$:
$$f(p, q) = p \times p \times \cdots \times p \quad (q \text{ terms}) = p^q; \quad f(p, 1) = p$$
$$g(p, q) = p^{p^{p^{\cdot^{\cdot^{\cdot}}}}} \quad (\text{up to } q \text{ terms}); \quad g(p, 1) = p$$
Which one of the following options is correct based on the above?
Scientific schematic diagram reproduced from official IIT paper
Options:
- (A) $f(2, 2) = g(2, 2)$
- (B) $f(g(2, 2), 2) < f(2, g(2, 2))$
- (C) $g(2, 1) \ne f(2, 1)$
- (D) $f(3, 2) > g(3, 2)$