Question

$f:N\to N$, where $f\left(x\right)=x-(-1{)}^x$, 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

The correct option is C one-one and onto

$f\left(x\right)=x-(-1{)}^x$
$f\left(x_1\right)=f\left(x_2\right)$
$\Rightarrow x_1=x_2$
In the above function
$f\left(2n\right)=2n-1$ and $f(2n-1)=2n$
$nϵN$.
Hence the above function is one one function.
Also, each point in the co-domain is the value of $f\left(x\right)$.
Hence the above function is one one and onto function.