Give an example of a function which is one-one but not onto. which is not one-one but onto. (iii) which is neither one-one nor onto.

Answer

N/a

Explanation

Let `f:N to N`, be a mapping defined by `f(x)=2x`
which is one-one.
For `f(x_(1))=f(x_(2))`
`implies 2x_(1)=2x_(2)`
`" " x_(1)=x_(2)`
Further f is not onto, as for `1 in N,` there does not exist any x is N such that `f(x)=2x+1.`
(ii) Let `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. f is not one-one as `f(1)=f(2)=1.` But f is onto.
(iii) The mapping `f: R to R` defined as `f(x)=x^(2)`, is neither one-one nor onto.