Q.

Let f:R→R, be defined as f(x)=ex2+cos⁡x, then f is

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a

one-one and onto

b

one-one and into

c

many-one and onto

d

many-one and into

answer is D.

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Detailed Solution

fx = ex2+cos x is even function , so it is not one-one i.e many one also fx is not onto since ex2≥1 ⇒ex2+cosx >0   Range of fx is 0,∞  which is not equal to codomain R   hence  f is into
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