Question
Consider the following statements in respect of the function f(x)=x in the interval (-1,1) : I. The function attains maximum value. II. The function attains minimum value. Which of the statements given above is/are correct ?
NDA
Mathematics
Functions
2026
NDA 2026 (Phase 1)
NDA Mathematics Question (2026) — Solution
Options
- A. I only
- B. II only
- C. Both I and II
- D. Neither I nor II
Answer
D. Neither I nor II
Step-by-step solution
Given the function f(x) = x defined on the open interval (-1, 1). For any x (-1, 1), we have -1 Since the interval is open, x can be arbitrarily close to 1 but never equals 1. Thus, f(x) does not attain a maximum value in the given interval. Similarly, x can be arbitrarily close to -1 but never equals -1. Thus, f(x) does not attain a minimum value in the given interval. Therefore, neither statement I nor statement II is correct. Answer: Neither I nor II
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