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JEE Main & Advanced Mathematics Functions Question Bank Critical Thinking

  • question_answer
    The  range of the function \[f(x){{=}^{7-x}}{{P}_{x-3}}\] is [AIEEE 2004]

    A) {1, 2, 3, 4, 5}

    B) (1, 2, 3, 4, 5, 6)

    C) {1, 2, 3, 4}

    D) {1, 2, 3}

    Correct Answer: D

    Solution :

    • For \[^{7-x}{{P}_{x-3}}\]to be defined, \[7-x>0\Rightarrow x<7\]                   
    • \[x-3\ge 0\Rightarrow x\ge 3\]; \[7-x\ge x-3\Rightarrow x\le 5\]                   
    • \ \[x\in \left\{ 3,\,4,\,5 \right\}\]Þ \[f(3)=1,\ f(4)=3,\,\,f(5)=2\]                   
    • So, the range of function \[=\left\{ 1,\,\,2,\,\,3 \right\}\].


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