The function `f(x) =e^(absx)` is

Options

A. continuous everywhere but not differentiable at x = 0
B. continuous and differentiable everywhere
C. not continuous at x = 0
D. None of the above

Answer

A

Explanation

Let ` u (x) = |x| and v (x) = e^(x)`
` therefore f(x) = vou(x) = v[u(x)]= v (|x|) = e^(|e|)`
Since , u(x) and and v(x) are both continous functions .
So, f(x) is also continuous function But ` u (x) = |x| ` is not
differentiable at x = 0 , whereas ` v (x) = e^(x)` differentiable at everywhere.
Hence , f(x) is continous everywhere but not differentiable at x = 0