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Show that if f: A to B and g : B to C ar...

Show that if `f: A to B and g : B to C` are onto, then `gof A to C` is also onto.

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Show that if f : A to B and g: B to C are one-one, then gof: A to C is also one-one.

Show that if f: A to B and g: B to C are one-one, then g of : A to C is also one-one.

Knowledge Check

  • Let f: A rarr B and g : B rarr C be the bijective funtions. Then (gof)^-1 is

    A
    1.`f^-1og^-1`
    B
    2.fog
    C
    3.`g^-1of^-1`
    D
    4.gof

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    Show that if f: AtoB and g: Bto C are onto,then go f : AtoC is also onto.

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    Let f: X to Y and g: Y to Z be two invertible functions. Then gof is also invertible with (gof)^(-1) = f^(-1)og^(-1) .

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