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JEE Main & Advanced JEE Main Paper Phase-I (Held on 08-1-2020 Morning)

  • question_answer
    Let f: \[R\to R\] be such that for all \[x\in R({{2}^{1+x}}+{{2}^{1-x}}),\] \[f(x)\] and \[({{3}^{x}}+{{3}^{-x}})\] are in A.P., then the minimum value of f(x) is              [JEE MAIN Held On 08-01-2020 Morning]

    A) 2                     

    B) 0

    C) 3         

    D) 4

    Correct Answer: C

    Solution :

    [c] For A.P \[2.f(x)=({{2}^{1-x}}+{{2}^{1+x}})+({{3}^{x}}+{{3}^{-x}})\] \[\Rightarrow f(x)={{2}^{x}}+{{2}^{-x}}+\frac{{{3}^{x}}+{{3}^{-x}}}{2}\] By AM-GM inequality \[{{2}^{x}}+{{2}^{-x}}\ge 2\] and \[{{3}^{x}}+{{3}^{-x}}\ge 2\] at x = 0 \[\therefore f(x)\ge 2+1\] \[f(x)\ge 3\]        


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