Question

Assertion :if $f\left(x\right)=|x-2|+|x-4|+|x-6|$ is an identify function for $4<x<6$. Reason: $f:A\to A$, defined by $f\left(x\right)=x$ is an identify 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

$f\left(x\right)=|x-2|+|x-4|+|x-6|$

$\Rightarrow f\left(x\right)=(x-2)+(x-4)-(x-6)=x$, since $4<x<6$

Hence, $f\left(x\right)$ is an identity function in the given interval.