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If f:NrarrZ f(n)={(n-1)/2; when n is od...

If `f:NrarrZ f(n)={(n-1)/2;` when n is odd `=-n/2;` when n is even Identify the type of function

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Show that the function f:N rarr Z, defined by f(n)=(1)/(2)(n-1) when n is odd ;-1/2 n when n is even is both one-one and onto

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Knowledge Check

  • Let f:N to Z and f (x)=[{:((x-1)/(2),"when x is odd"),(-(x)/(2),"when x is even"):}, then:

    A
    f (x) is bijective
    B
    f (x) is injective but not surjective
    C
    f (x) is not injective but surjective
    D
    f (x) is neither injective nor subjective

  • If a, b,c, in _N, a^(n) + b^(n) is divisible by c when n is odd but not when n is even, then value of c is

    A
    a+ b
    B
    a-b
    C
    `a^(3)+b^(3)`
    D
    `a^(3)+b^(3)`

  • If f:NrarrZ defined as f(n)={{:((n-1)/(2),":"," if n is odd"),((-n)/(2),":", " if n is even"):} and g:NrarrN defined as g(n)=n-(-1)^(n) , then fog is (where, N is the set of natural numbers and Z is the set of integers)

    A
    one - one and onto
    B
    one - one and into
    C
    many - one and onto
    D
    many - one and into

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