JEE Main & Advanced Mathematics Functions Question Bank Self Evaluation Test - Relations and Functions-I

  • question_answer
    If \[f(x)=4x-{{x}^{2}},x\in R,\] then \[f(a+1)-f(a-1)\] is equal to

    A) \[2(4-a)\]

    B)        \[4(2-a)\]

    C) \[4(2+a)\]

    D)        \[2(4+a)\]

    Correct Answer: B

    Solution :

    [b] \[f(x)=4x-{{x}^{2}}\] \[\Rightarrow f(a+1)-f(a-1)=\{4(a+1)-{{(a+1)}^{2}}\}\] \[-\{4(a-1)-{{(a-1)}^{2}}\}\] \[=8-\{{{(a+1)}^{2}}-{{(a-1)}^{2}}\}=8-4a=4(2-a)\]


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