Question

Consider the following functions for non-zero positive integers, \( p \) and \( q \):
\[ f(p, q) = p \times p \times p \times \cdots \times p = p^q \quad ; \quad f(p, 1) = p \] \[ g(p, q) = ppppp\cdots (up \text{ to } q \text{ terms}) \quad ; \quad g(p, 1) = p \] Which one of the following options is correct based on the above?

• A. \( f(2,2) = g(2,2) \)
• B. \( f(g(2,2), 2)<f(2, g(2,2)) \)
• C. \( g(2,1) \neq f(2,1) \)
• D. \( f(3,2)>g(3,2) \)

Hint:

When evaluating such functions, carefully check the structure of each formula and evaluate them step by step to avoid errors.

Answer 1

The Correct Option is A

Let us first evaluate \( f(2, 2) \) and \( g(2, 2) \).
Step 1: Evaluate \( f(2, 2) \)
From the given formula for \( f(p, q) \): \[ f(2, 2) = 2 \times 2 = 2^2 = 4. \] Step 2: Evaluate \( g(2, 2) \)
From the given formula for \( g(p, q) \): \[ g(2, 2) = 2 \times 2 = 2^2 = 4. \] Step 3: Compare the results.
Since \( f(2, 2) = 4 \) and \( g(2, 2) = 4 \), we conclude that \( f(2, 2) = g(2, 2) \). Therefore, the correct answer is (A).