Question

Assertion :$f\left(x\right)=\sqrt{x-3}+\sqrt{3-x}$ is continuous at $x=3$. Reason: $f\left(x\right)$ is a fixed number

• 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 incorrect and Reason is correct
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is C Assertion is incorrect and Reason is correct

Let $f\left(x\right)=g\left(x\right)+p\left(x\right)$

Such that $g\left(x\right)=\sqrt{(}x-3)$ and $p\left(x\right)=\sqrt{3-x}$

$g\left(x\right)$ is defined for $x\ge 3$

$p\left(x\right)$ is defined for $x\le 3$

Therefore, $f\left(x\right)$ is defined for only $x=3$

Therefore $f\left(3\right)=f\left(x\right)=0$ and is a fixed number at discontinuous at $x=3$

A is incorrect and R is correct.