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

  • question_answer
    Let \[f(x)=x,g(x)=\frac{1}{x}\] and \[h(x)=f(x)g(x).\]Then, \[h(x)=1\] if and only if

    A) x is a real number

    B) x is a rational number

    C) x is an irrational number

    D) x is a non-zero real number

    Correct Answer: D

    Solution :

    [d] \[D(f)=R,D(g)=R-\{0\}\] \[\therefore D(h)=R-\{0\}\] and \[h(x)=f(x)g(x)=x\times \frac{1}{x}=1\] \[\therefore h(x)=1\] if and only if \[x\in R-\{0\}\]


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