JEE Advanced 2014 Mathematics question
Let , , and be defined by
=
;
=
and
=
List II P. is Q. is R. is S. is List I 1. onto but not one-one 2. neither continuous nor one-one 3. differentiable but not one-one 4. continuous and one-one
Answer: (D)
Solution
P: for x < 0 (values in (0, ∞)) and for x ≥ 0 (values in [0, ∞)); its range is [0, ∞) = codomain (onto), but values are repeated, so not one-one → 1. Q: is continuous at 0 and both one-sided derivatives there equal 1 (), so it is differentiable; but sin x for x < 0 repeats
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