Q. 875.0( 1 Vote )

The function f(x) = e|x| is
A. continuous everywhere but not differentiable at x = 0

B. continuous and differentiable everywhere

C. not continuous at x = 0

D. none of these

Answer :

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.

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