Question

Assertion :$f:N\to I$ be a function defined by $f\left(x\right)=x-400$ is an into function. Reason: $f$ is not an onto function.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Let $f\left(x\right)=y=x-400$

$\Rightarrow x=y+400=g\left(y\right)$ (say)

Here $g\left(y\right)$ is defined for $y\in I$

$g\left(y\right)\ne Nfory\le -400$

Therefore $y$ is not onto function, now if a function is not onto then it must be into function.