Question

If $f\left(x\right)=\{\begin{array}{c}2x+b\text{if}x<a\\ x+d\text{if}x\ge a\end{array}$ and $\underset{x\to a}{lim}f\left(x\right)=l,$ then $l$ is equal to

• A. $b+d$
• B. $b-d$
• C. $2d+b$
• D. $2d-b$

Answer 1

The correct option is D $2d-b$

$\underset{x\to a}{lim}f\left(x\right)=l$
$\Rightarrow \underset{x\to a^{-}}{lim}(2x+b)=\underset{x\to a^{+}}{lim}(x+d)=l$
$\therefore l=2a+b\cdots \left(1\right)$ and
$l=a+d\cdots \left(2\right)$
By eleminating $a$ from $\left(1\right)$ and $\left(2\right),$ we get
$l=2d-b$