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Question
The function f(x) = `"e"^|x|` is ______.
Options
Continuous everywhere but not differentiable at x = 0
Continuous and differentiable everywhere
Not continuous at x = 0
None of these
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Solution
The function f(x) = `"e"^|x|` is continuous everywhere but not differentiable at x = 0.
Explanation:
Given that: f(x) = `"e"^|x|`
We know that modulus function is continuous but not differentiable in its domain.
Let g(x) = |x| and t(x) = ex
∴ f(x) = got(x) = g[t(x)] = `"e"^|x|`
Since g(x) and t(x) both are continuous at x = 0 but f(x) is not differentiable at x = 0.
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