JEE Main & Advanced Mathematics Functions Question Bank Self Evaluation Test - Relation and Functions-II

  • question_answer
    Let \[f:R\to R\] be a function such that \[f(x)=ax+3sinx+4cosx.\] Then f(x) is invertible if

    A) \[a\in (-5,5)\]

    B) \[a\in (-\infty ,-5)\]

    C) \[a\in (0,+\infty )\]

    D) None of these

    Correct Answer: B

    Solution :

    [b] \[f'(x)=a+3\cos x+4\sin x\] \[f(x)\] is one-one if \[f'(x)>0\] for all x or \[f'(x)<0\]for all x. So, \[f'(x)<0\forall x,\] if \[a<-5\] and \[f'(x)>0\forall x,\] if \[a>5\] \[\therefore \,\,\,a\in (-\infty ,-5)\cup (5,\infty )\]


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