Q. 875.0( 1 Vote )

# The function f(x) = e|x| isA. continuous everywhere but not differentiable at x = 0B. continuous and differentiable everywhereC. not continuous at x = 0D. none of these

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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