Properties of Periodic Function

Q.

The period of the function $f\left(x\right)=\left|\sin \left(x\right)\right|+\left|\cos \left(x\right)\right|$ is:

1. $\mathrm{\pi }$

2. $\frac{\mathrm{\pi }}{2}$

3. $2\mathrm{\pi }$

4. None of these

Q. The graph of the function y = f(x) is symmetrical about the line x = 2, then

1. f ( x+2) = f (x - 2)
2. f (2 + x) =f (2 - x)
3. f(x) = f(-x)
4. f(x) = - f(-x)

Q.

The period of the function $f\left(x\right)=\sin \left(4x\right)+\cos \left(4x\right)$ is:

1. $\mathrm{\pi }$

2. $\frac{\mathrm{\pi }}{2}$

3. $2\mathrm{\pi }$

4. None of these

Q.

If $\mathrm{f}:\mathrm{R}\to \mathrm{C}$ is defined by $\mathrm{f}\left(\mathrm{x}\right)={\mathrm{e}}^{2\mathrm{ix}}$ for x belongs to $R$, then $f$ is (where $C$ denotes the set of all complex numbers)

1. One-one

2. Onto

3. One-one and onto

4. Neither one-one nor onto

Q.

If a function defined on f : R $\to$ R with 6 as the period of the f(x). If f(0) = 13 then find f(96) ?

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Q. graph of f(x)=x+1 is