Q. 875.0( 1 Vote )

# The function f(x)

Given that, f(x) = e|x|

Let g(x) = |x| and h(x) = ex

Then, f(x) = hog(x)

We know that, modulus and exponential functions are continuous everywhere.

Since, composition of two continuous functions is a continuous function.

Hence, f(x) = hog(x) is continuous everywhere.

Now, v(x)=|x| is not differentiable at x=0.

Lv’(0) =

=

= ( v(x) = |x|)

=

=

=

Rv’(0) =

=

= ( v(x) = |x|)

=

=

=

Lv’ (0) ≠ Rv’(0)

|x| is not differentiable at x=0.

So, e|x| is not differentiable at x=0.

Hence, f(x) continuous everywhere but not differentiable at x = 0.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

Show that of all Mathematics - Board Papers

Find the value ofMathematics - Board Papers

If x sin (a + y) Mathematics - Exemplar

The function f(x)Mathematics - Exemplar

Show that of all Mathematics - Board Papers

If the function fMathematics - Board Papers

Find <img wMathematics - Exemplar

Let f(x) = |sinx|Mathematics - Exemplar

The derivative ofMathematics - Exemplar