MCQ
A function $f: R \rightarrow R$ is defined by:
$f(x)=\left\{\begin{array}{cc}e^{-2 x}, & x<\ln \frac{1}{2} \\ 4, & \ln \frac{1}{2} \leq x \leq 0 \\ e^{-2 x}, & x>0\end{array}\right.$
Which of the following statements is true about the function at the point $x=\ln \frac{1}{2}$ ?
$f(x)=\left\{\begin{array}{cc}e^{-2 x}, & x<\ln \frac{1}{2} \\ 4, & \ln \frac{1}{2} \leq x \leq 0 \\ e^{-2 x}, & x>0\end{array}\right.$
Which of the following statements is true about the function at the point $x=\ln \frac{1}{2}$ ?
- A$f(x)$ is not continuous but differentiable.
- ✓$f(x)$ is continuous but not differentiable.
- C$f(x)$ is neither continuous nor differentiable.
- D$f(x)$ is both continuous as well as differentiable.