Which one of the following statements is NOT CORRECT ? - Vidyadip

MCQ

Which one of the following statements is NOT CORRECT ?

A
The derivative of a diffrentiable periodic function is a periodic function with the same period.
✓
If $f (x)$ and $g (x)$ both are defined on the entire number line and are aperiodic then the function $F(x) = f (x) . g (x)$ can not be periodic.
C
Derivative of an even differentiable function is an odd function and derivative of an odd differentiable function is an even function.
D
Every function $f (x)$ can be represented as the sum of an even and an odd function

✓

Answer

Correct option: B.

If $f (x)$ and $g (x)$ both are defined on the entire number line and are aperiodic then the function $F(x) = f (x) . g (x)$ can not be periodic.

b
For : consider $f (x) =x - \,\sqrt {{x^2} + 1} $ and $g (x) =x + \,\sqrt {{x^2} + 1} $ then $ F(x) = 1$ which is periodic $==>$ False]

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