Question

Let $f:N\to Z$ be a function defined as $f\left(x\right)=x-1000.$ Then which of the following is true?

• A. $f\left(0\right)=-1000$
• B. $f\left(100\right)=0$
• C. $f$ is a many-one function
• D. None of these

Answer 1

The correct option is D None of these

$f\left(0\right)=-1000$ is not true as $0\notin N$
and
$f\left(100\right)=-900$
Let $f\left(x_1\right)=f\left(x_2\right),x_1,x_2\in N$
$\Rightarrow x_1-1000=x_2-1000$
$\Rightarrow x_1=x_2$
Hence, $f$ is a one-one function.