Question

$f\left(x\right)=\{\begin{array}{c}3x-8\text{if}x\le 5\\ 2k\text{if}x>5\end{array}$ is continuous, find $k.$

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

Answer 1

The correct option is D $\frac{7}{2}$

Since $f$ is continuous,
$f\left(5^{-}\right)=f\left(5^{+}\right)=f\left(5\right)$
$\Rightarrow 3\times 5-8=2k$
$\Rightarrow k=\frac{7}{2}$