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Which of the following function from Z t...

Which of the following function from Z to itself are bijections?

A

`f(x)=x^3`

B

`f(x)=x+2`

C

`f(x)=2x+1`

D

`f(x)=x^2+x`

Text Solution

Verified by Experts

The correct Answer is:
B
(b) Clearly, `f(x)` must be `x+2` as for this function, each image has its preimage and each image has one and only one preimage.
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Knowledge Check

  • Which of the following functions from l to itself are bijections?

    A
    `f(x) = x^(3)`
    B
    `f(x) = x + 2`
    C
    `f(x) = 2x + 1`
    D
    `f(x) = x^(2) + x`

  • Which of the following functions from Z into Z are bijections?

    A
    `f(x)=x^(3)`
    B
    `f(x)=x+2`
    C
    `f(x)=2x+1`
    D
    `f(x)=x^(2)+1`

  • Let A = [-1, 1]. Which of the following functions on A is not a bijection?

    A
    `f(x) = x[x]`
    B
    `f(x) = x^(3)`
    C
    `f(x) = sin(pi/2x)`
    D
    `f(x) = cos(pi/2.x)`

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