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JEE Main & Advanced Mathematics Functions Question Bank Functions

  • question_answer
    If \[f(x)=ax+b\] and \[g(x)=cx+d\], then \[f(g(x))=g(f(x))\] is equivalent to [UPSEAT 2001]

    A)            \[f(a)=g(c)\]

    B)            \[f(b)=g(b)\]

    C)            \[f(d)=g(b)\]

    D)            \[f(c)=g(a)\]

    Correct Answer: C

    Solution :

               We have \[f(x)=ax+b,\,g(x)=cx+d\]                    and \[f(g(x))=g(f(x))\]            Þ \[f(cx+d)=g(ax+b)\] Þ \[a[cx+d]+b=c[ax+b]+d\]                    Þ \[ad+b=cb+d\]Þ \[f(d)=g(b)\].


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