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f:RrarrR" defined by "f(x)=(1)/(2)x|x|+c...

`f:RrarrR" defined by "f(x)=(1)/(2)x|x|+cos+1` is

A

one-one and onto

B

one-one and into

C

many-one and onto

D

many-one and into

Text Solution

Verified by Experts

The correct Answer is:
A
Clearly `f(x)rarroo` when `x rarroo`
and `f(x)rarr-oo` when `x rarr-oo`
`therefore" Range is R as f(x) os continuous"`.
Also for `x ge f'(x)=|x|-sin x ge 0`
`therefore" f(x) is increasing"`
`therefore" f(x) is one-one."`
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