Question

If $f\left(x\right)=\{\begin{array}{c}mx-1,x\le 5\\ 3x-5,x>5\end{array}$ is continuous then value of m is:

• A. $\frac{11}{5}$
• B. $\frac{5}{11}$
• C. $\frac{5}{3}$
• D. $\frac{3}{5}$

Answer 1

The correct option is A $\frac{11}{5}$

$f\left(x\right)\{\begin{array}{cc}mx-1& \text{if}x\le 5\\ 3x-5& \text{if}x>5\end{array}$

Since the function is continuous at $x=5$.

Therefore,

${lim}_{x\to 5^{-}}f\left(x\right)={lim}_{x\to 5^{+}}f\left(x\right)=f\left(5\right)$

${lim}_{x\to 5^{-}}(mx-1)={lim}_{x\to 5^{+}}(3x-5)$

$5m-1=15-5$

$5m=10+1$

$\Rightarrow m=\frac{11}{5}$

Hence the value of $m$ is $\frac{11}{5}$.