Question

Assertion :Let $f\left(x\right)=\{\begin{array}{cc}1& \text{if}2\le x\le 3\\ 3& \text{if}3\le x\le 5\end{array}$

The mean value of $f$ is attained

Reason: $f$ is a bounded function but not continuous on $[2,5]$

• A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion
• B. Both Assertion & Reason are individually true but Reason is not the ,correct (proper) explanation of Assertion
• C. Assertion is true but Reason is false
• D. Assertion is false but Reason is true

Answer 1

The correct option is D Assertion is false but Reason is true

${lim}_{x\to 3^{-}}f\left(x\right)=1$

${lim}_{x\to 3^{+}}f\left(x\right)=3$

LHL$\ne$RHL $\therefore f\left(x\right)$ is discontinuous

$\Rightarrow$Average value cannot be attained.