Question

If the function
$f\left(x\right)=\{\begin{array}{c}k+x,\text{for}x<1\\ 4x+3,\text{for}x\ge 1\end{array}$
is continuous at $x=1$, then $k=$

• A. $7$
• B. $8$
• C. $6$
• D. $-6$

Answer 1

The correct option is C $6$

Given, $f\left(x\right)$ is continuous at $x=1$
$\therefore \underset{x\to 1^{-}}{lim}f\left(x\right)=\underset{x\to 1^{+}}{lim}f\left(x\right)=f\left(1\right)$
Hence, $\underset{x\to 1^{-}}{lim}(k+x)=\underset{x\to 1^{+}}{lim}(4x+3)$
$\therefore k+1=4\left(1\right)+3$
$\therefore k=7-1$
$\therefore k=6$
Hence, the correct answer from the given alternative is option C.