$f: N \rightarrow N, f(x) = x^3$ is . . . . . . .

The function $f: N \rightarrow Z$ defined by $f(n) = \begin{cases} \frac{n}{2} & , n \text{ is even} \\ -\left(\frac{n-1}{2}\right) & , n \text{ is odd} \end{cases}$ is . . . . . . .

Let $f: R \rightarrow R$ be defined as $f(x)=x^{4}$. Choose the correct answer.

Let the functions $f$ and $g$ be $f: [0, \frac{\pi}{2}] \rightarrow R$ given by $f(x) = \sin x$ and $g: [0, \frac{\pi}{2}] \rightarrow R$ given by $g(x) = \cos x$,where $R$ is the set of real numbers. Consider the following statements:
Statement $(I)$: $f$ and $g$ are one-one.
Statement $(II)$: $f+g$ is one-one.
Which of the following is correct?

Function $f: R \rightarrow R$ defined by $f(x) = x^3$ is . . . . . . .

Check the injectivity and surjectivity of the function $f: R \rightarrow R$ defined by $f(x) = x^2$.