Given,
f(x)=x2+1x2+2x+1
f′(x)=(x2+1)2(x2+1)(2x+2)−(x2+2x+1)2x
⇒f′(x)=(x2+1)22x3+2x2+2x+2−2x3−4x2−2x
⇒f′(x)=(x2+1)22(1−x2)=−(x2+1)22(x+1)(x−1)
Clearly f(x) is one-one in (−∞,−1) and also in (1,∞) but f(x) is not one-one in (−∞,∞)
Let f:R→ R be a function such that f(x)= x^2+2x+1 x^2+1. Then
JEE Main 2023 — Mathematics Algebra
2023mcqmedium
Let f:R→R be a function such that f(x)=x2+1x2+2x+1. Then
Official previous-year question
Held on 29 Jan 2023 · Verified 6 Jul 2026.
Options
- A
f(x) is many-one in (−∞,−1)
- B
f(x) is many-one in (1,∞)
- C
f(x) is one-one in [1,∞) but not in (−∞,∞)
- D
f(x) is one-one in (−∞,∞)
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