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Let a function f:R to R be defined by f...

Let a function `f:R to R` be defined by `f(x)=2x+cosx+sinx " for " x in R`. Then find the nature of `f(x)`.

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The correct Answer is:
bijective
We have `f(x)=2x+cos x +sin x`
` :. f'(x)=2-sinx+cosx gt 0 AA x in R.`
Also, `f(x)` exists continuously.
Hence `f(x)` is one-one.
Clearly range of `f(x)` is R.
Therefore `f(x)` is onto.
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