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12th Class Mathematics Relations and Functions Question Bank Case Based (MCQs) - Relations and Functions

  • question_answer
    Directions : (21 - 25)
    Raji visited the Exhibition along with their family. The Exhibition had a huge swing, which attracted many children. Raji found that the swing traced the path of a Parabola as given by \[y={{x}^{2}}\].
    Answer the following questions using the above information.
    Let \[f\,:\,R\to R\] be defined by \[f\left( x \right)={{x}^{2}}\]is

    A) Neither Surjective nor Injective

    B) Surjective

    C) Injective

    D) Bijective

    Correct Answer: A

    Solution :

    \[y={{x}^{2}}\] From \[x=-1,\,\,y=1\] \[x=1,\,\,y=1\] \[\therefore \,\,\,f\left( x \right)\] is not injective For \[y=2,\,\,{{x}^{2}}=2\] Also f(x) is not onto.


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