Question

If $N\to N$ is defined by $f\left(n\right)=n-(-1{)}^n$ , then

• A. f is one-one but not onto
• B. f is both one-one and onto
• C. f is neither one-one nor onto
• D. f is onto but not one-one

Answer 1

The correct option is B f is both one-one and onto

This function f maps
$1\to 2,2\to 1$
$3\to 4,4\to 3$
$5\to 6,6\to 5$
i.e., $2m-1\to 2m$ and $2m\to 2m-1$
So f is one-one and onto.