If f:R→R given by $$f(x)=ax+$$$$sin$$⁡$$x+a$$, then f is $$one-one$$ and onto for all

Correct option is 2a∈R~[-1,1]

Questions

If $f : R \to R$ given by $f (x) = a x + \sin x + a,$ then $f$ is one-one and onto for all

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a∈R

a∈R~[-1,1]

a∈R~{0}

a∈R~{-1}

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detailed solution

Correct option is B

For a≠0, the range of f is R. f is differentiable function so f is one-one and only if f is monotonic. f′(x)=a+cos⁡xIf a>1, f'(x)>0 i.e. f is increasingIf a<-1, f'(x)<0 i.e. f is decreasing Thus f is monotonic if a∈R~[-1,1].

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If f:R→R given by f(x)=ax+sin⁡x+a, then f is one-one and onto for all

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If $f : R \to R$ given by $f (x) = a x + \sin x + a,$ then $f$ is one-one and onto for all