Q.8
Given that f(y) = |y| / y, and y is any non-zero real number,
the value of f(q) − f(−q) is
Options:
(A) 0
(B) −1
(C) 1
(D) 2
Introduction
Modulus-based functions are common in competitive exams such as
JEE, CUET, NDA, and Class 11–12 Mathematics. This problem tests
understanding of function behavior for positive and negative values.
Understanding the Function
The function f(y) = |y| / y behaves as:
- If y > 0, then f(y) = 1
- If y < 0, then f(y) = −1
Step-by-Step Solution
Case 1: q > 0
f(q) = 1
f(−q) = −1
|f(q) − f(−q)| = |1 − (−1)| = |2| = 2
Case 2: q < 0
f(q) = −1
f(−q) = 1
|f(q) − f(−q)| = |−1 − 1| = |−2| = 2
Correct Answer
Option (D): 2
Conclusion
Since q and −q always have opposite signs, the function values differ
by 2. Therefore, the value of
|f(q) − f(−q)| is always 2.
