Question

If $f:N\to N$ where $f(x)=x-(-1{)}^x$, then $f$ is

• A. one one and into
• B. many-one and into
• C. one-one and onto
• D. many-one and onto

Answer 1

Answer: (C)

$x=\{1,2,3,$..............
If $x=2n,n\in N$ then
$f(x)=x-1$
$f(x)\in \{1,3\dots \dots \dots \dots \dots \}$
If $x=2n-1,n\in Nf(x)=x+1$ then $f(x)\in \{2,4$,........