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JEE Main & Advanced Mathematics Functions Question Bank Functions

  • question_answer
    If \[f(x)=a\cos (bx+c)+d\], then range of \[f(x)\] is            [UPSEAT 2001]

    A)                    \[[d+a,\ d+2a]\]

    B)             \[[a-d,\ a+d]\]

    C)            \[[d+a,\ a-d]\]

    D)            \[[d-a,\ d+a]\]

    Correct Answer: D

    Solution :

               \[f(x)=a\cos (bx+c)+d\]                                     ?..(i)            For minimum \[\cos (bx+c)=-1\]            from (i), \[f(x)=-a+d=(d-a)\]            For maximum \[\cos (bx+c)=1\]            from (i), \[f(x)=a+d=(d+a)\]                    \Range of \[f(x)=[d-a,\,\,d+a]\].


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