Question

$iff:N\to Nisdefinedbyf\left(n\right)=n-(-1{)}^n,then$

• 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

$1\to 2,2\to 13\to 4,4\to 35\to 6,6\to 5i.e.,2m-1\to 2mand2m\to 2m-1$
So, f is one-one and onto.