JEE Main & Advanced Mathematics Functions Question Bank Functions

  • question_answer
    If \[f(x)=4{{x}^{3}}+3{{x}^{2}}+3x+4\], then \[{{x}^{3}}f\left( \frac{1}{x} \right)\] is            [SCRA 1996]

    A)            \[f(-x)\]

    B)            \[\frac{1}{f(x)}\]

    C)            \[{{\left( f\left( \frac{1}{x} \right) \right)}^{2}}\]

    D)            \[f(x)\]

    Correct Answer: D

    Solution :

               \[{{x}^{3}}f\left( \frac{1}{x} \right)={{x}^{3}}\,\left[ \frac{4}{{{x}^{3}}}+\frac{3}{{{x}^{2}}}+\frac{3}{x}+4 \right]\] \[=4+3x+3{{x}^{2}}+4{{x}^{3}}=f(x)\].


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