Question

$f\left(x\right)=\{\begin{array}{cc}3x-8& ifx\le 5\\ 2k& ifx>5\end{array}$ is continuous, find $k$

• A. $\frac{2}{7}$
• B. $\frac{3}{7}$
• C. $\frac{4}{7}$
• D. $\frac{7}{2}$

Answer 1

Answer: (D)

$\frac{7}{2}$

For the function $f\left(x\right)$ to continuous at $x=5$

We must have, $\underset{x\to 5^{-}}{lim}f\left(x\right)=\underset{x\to 5^{+}}{lim}f\left(x\right)=f\left(5\right)$

$\Rightarrow \underset{x\to 5}{lim}(3x-8)=\underset{x\to 5}{lim}\left(2k\right)$

$\Rightarrow 3\times 5-8=2k$

$\therefore k=\frac{7}{2}$