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Show that the function f:N to N, given b...

Show that the function `f:N to N,` given by `f (1) =f (2) =1 and f (x) =x -1,` for every `x gt 2,` is onto but not one-one.

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The correct Answer is:
`f (1) =1`
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Show that the function f: N to N, given by f (x) =2x, is one-one but not onto.

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Knowledge Check

  • If f : N to R is defined by f(1) = -1 and f(n+1)=3f(n)+2 for n gt 1 , then f is

    A
    one - one
    B
    onto
    C
    a constant function
    D
    `f(n)gt 0` for `n gt 1`

  • If f is function such that f(0)=2, f(1)=3 and f(x+2)=2f(x)-f(x+1) for every real x, then f(5) is

    A
    7
    B
    13
    C
    1
    D
    5

  • If f : N to R is defined by f(1)=-1 and f(n+1)=3f(n) +2 for n gt 1 , then f is:

    A
    one-one
    B
    onto
    C
    a constant function
    D
    `f(n) gt 0` for `n gt 1`

    • Similar Questions

    Explore conceptually related problems

    Show that the Signum Function f: R to R, given by f (x) ={{:(1, if x gt 0), ( 0, if x =0),(-1, if x lt0):} is neither one-one nor onto.

    Show that f:Nto N, given by x + 1, if x is odd, f (x) = x -1, if x is even is both one-one and onto.

    Show that the function f : R to R {x in R : -1 lt x lt 1} defined by f (x) = (x)/(1 + |x|), x in R is one one and onto function.

    Is the function f , defined by f(x) = {:{(x^(2) if x le 1), (x if x gt 1):} continuous on R ?

    Determine whether the function f:R to R defined by f(x) = x^(2) is one one (or) onto (or) bijection.

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