Given that f(y) = |y| / y, and q is any non-zero real number, the value of |f(q) − f(−q)| is
Options:
(A) 0
(B) −1
(C) 1
(D) 2
Official Answer Key:
D
Step-by-Step Solution & Explanation
f(y) = |y|/y = sign(y): +1 if y>0, −1 if y<0. For any non-zero q, f(q) and f(−q) always have opposite signs (one is +1, the other −1), regardless of q's own sign. So f(q) − f(−q) = (±1) − (∓1) = ±2, and |f(q)−f(−q)| = 2, matching option (D). (Note: option (B), −1, is not achievable since the expression is wrapped in an absolute value and can only equal 0 or 2 — verified for both q>0 and q<0 cases.)
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.