A function f: R R is defined by: f(x)= cc e^ -2 x , & x< 1 2 4, &… - Vidyadip

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 $x=\ln \frac{1}{2}$ ?

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.

✓

Answer

Correct option: B.

$f(x)$ is continuous but not differentiable.

$f(x)$ is continuous but not differentiable.

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