Question

Define $f:Z\to Z$

$f\left(x\right)=\{\begin{array}{c}\frac{x}{2}\left(xiseven\right)\\ 0\left(xisodd\right)\end{array}$ then $f$ is

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

Answer 1

The correct option is A onto but not one-one

$f:z\to z$

When $x$ is even

$f\left(x\right)=\frac{x}{2}$

$f\left(x\right)=0$ for $x$ is odd

so for all $x$ there is atleast one $y$

So, the function is onto
$f\left(x\right)$ for $x=1,2,3,......,(2n+1)$
for all odd $x$ there is only one $y=0$
So, the function is not one-one