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

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Alok Kumar Singh | Contributor-Level 10

a year ago

This is an Objective Answer Type Questions as classified in NCERT Exemplar

Sol:

$\begin{array}{l} G i v e n t h a t f (x) = e^{| x |} \\ W e k n o w t h a t modulus f u n c t i o n i s c o n t i n u o u s b u t n o t d i f f e r e n t i a b l e i n i t s d o m a i n . \\ L e t g (x) = | x | a n d t (x) = e^{| x |} \\ ∴ f (x) = g o t (x) = g [t (x)] = e^{| x |} \\ Since g (x) a n d t (x) b o t h a r e c o n t i n u o u s a t x = 0 b u t f (x) i s n o t d i f f e r e n t i a b l e a t x = 0 . \\ H e n c e, t h e c o r r e c t o p t i o n i s (a) \end{array}$

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