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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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Prove that the function f: R to R, given by f (x) =2x, is one-one and onto.

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Knowledge Check

  • The function f:X to Y defined by f(x)= sin x is one - one but not onto if X and Y are respectively equal to

    A
    IR and IR
    B
    `[0,pi]` and `[0, 1]`
    C
    `[0, (pi)/(2)]` and `[-1,1]`
    D
    `[(-pi)/(2),(pi)/(2)]` and `[-1, 1]`

  • The function f: X rarr Y defined by f(x)=sin x is one-one but not onto, if X and Y are respectively equal to

    A
    1)`[0, pi] and [0,1]`
    B
    2)`[-(pi)/(2), (pi)/(2)] and [-1,1]`
    C
    3)`[0, (pi)/(2)] and [-1,1]`
    D
    4)`R and R`

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    Show that the function f: R to R given by f (x) = x ^(3) is injective.

    Show that the Modulus function f : R to R given by f (x) = [x] is neither one-one nor onto.

    Show that the function given by f (x) = e ^(2x) is increasing on R.

    Show that the function given by f(x) = 7x – 3 is increasing on R.

    Show that the Modulus Functions f : R to R, given by f (x) =|x|, is neither one-one nor onto, whre |x| is x, if x is positive or 0 and |x| is -x, if x is negative.

    Show that the function f : N to N defined by f(x) = x^(2), AA x in N is injective but not surjective.

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