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Which of the following function from Z t...

Which of the following function from Z to itself are bijections? `f(x)=x^3` (b) `f(x)=x+2` `f(x)=2x+1` (d) `f(x)=x^2+x`

A

`f(x)=x^(3)`

B

`f(x)=x+2`

C

`f(x)=2x+1`

D

`f(x)=x^(2) +1`

Text Solution

Verified by Experts

The correct Answer is:
B
Here, `f(x) =x +2impliesf(x_(1))=f(x_(2))`
`x_(1)+2=x_(2)+2implies x_(1)=x_(2)`
Let `" " y=x+2`
`x=y-2 in Z, AA y in x`
Hence, f(x) is one-one and onto.
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