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11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-7

  • question_answer
    Let \[\mathbf{F}:\mathbf{R}\to \mathbf{R}\] be defined by \[f(x)=3x-4\] \[{{f}^{-1}}(x)\]

    A)  \[~\frac{x}{3}-4~\]                 

    B)  \[\frac{x+4}{3}\]         

    C)  \[3x+4\]                      

    D)  None of these

    Correct Answer: B

    Solution :

    [b] \[\because f\left( x \right)=3x-4\] \[y=3x-4\] \[3x=y+4\] \[x=\frac{y+4}{3}x={{f}^{-1}}(y)={{f}^{-1}}(x)=\frac{x+4}{3}\] Hence, option [b] is correct.


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