If a function $f: R \rightarrow R$ is defined by $f(x)=x^3-x$,then $f$ is

Let $X$ and $Y$ be subsets of $R$,the set of all real numbers. The function $f:X \to Y$ defined by $f(x) = x^2$ for $x \in X$ is one-one but not onto if (Here $R^+$ is the set of all positive real numbers):

If $f: R \rightarrow C$ is defined by $f(x)=e^{2 i x}$ for $x \in R$,then $f$ is (where $C$ denotes the set of all complex numbers)

Consider a function $f: [0, \frac{\pi}{2}] \rightarrow \mathbb{R}$ given by $f(x) = \sin x$ and $g: [0, \frac{\pi}{2}] \rightarrow \mathbb{R}$ given by $g(x) = \cos x$. Show that $f$ and $g$ are one-one,but $f + g$ is not one-one.

Let $A = \{(x, y) : 2x + 3y = 23, x, y \in N\}$ and $B = \{x : (x, y) \in A\}$. Then the number of one-one functions from $A$ to $B$ is equal to ................

If $f(x) = |\sin x| + |\cos x|$ and $g(x) = [x]$,then what is the period of $h(x) = g(f(x))$,where $[.]$ denotes the Greatest Integer Function $(G.I.F.)$?