Question

Example 20. If f(x) = 2 [x] + cos x, then f:R → R is Miyone-one and onto (2) one-one and into (3) many-one and into (4) many-one and onto​

Answer 1

Answer:

Correct option is

D

one- one onto

For cos(x)>0,f

′

(x)=2−sin(x)>0 (always)

For cos(x)<0,f

′

(x)=2+sin(x)>0 (always)

Since f

′

>0, therefore f is continuously increasing, therefore it is monotonic and one-one

range of 2x is complete R and range of ∣cos(x)∣ is [0,1], Hence 2x+∣cos(x)∣ has a range of R, therefore function is onto.

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