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The function f(x) = e^(|x|) is...

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 the above

Text Solution

Verified by Experts

The correct Answer is:
A
Let ` u(x) = |x|` and `v(x) = e^(x)`
`:. f(x) = vou(x)=v[u,(x)]`
` =v|x|=e^(|x|)`
Since, ` u(x)` and `v(x)` are both continuous functions.
So, ` f(x)` is also continuous function but ` u(x) = |x|` is not differentiable at `x = 0`.
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NCERT EXEMPLAR-CONTINUITY AND DIFFERENTIABILITY-Continuity And Differentiability
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  8. If y = sqrt(sinx+y), then (dy)/(dx) is equal to

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  14. Derivative of x^(2) w.r.t. x^(3) is "……."

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  16. For the curve sqrt(x) + sqrt(y) = 1, (dy)/(dx) at (1/4,1/4) is "……….".

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  17. Rolle's theorem is applicable for the function f(x) = |x-1| in [0,2].

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  18. If f is continuous on its domain D; then |f| is also continuous on D

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  19. If f is continuous on its domain D; then |f| is also continuous on D

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  20. The composition of two continuous function is a continuous function.

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