Let $f: R \to R$ be defined as $f(x) = x^3$. Then $f$ is . . . . . . .

If $f: R \rightarrow R$,such that $f(x)=\frac{e^{x}+e^{-x}}{e^{x}-e^{-x}}$,then $f$ is

Let $A$ be the set of all $50$ students of Class $X$ in a school. Let $f: A \rightarrow N$ be a function defined by $f(x) = \text{roll number of the student } x$. Show that $f$ is one-one but not onto.

Let $A \subseteq R, B \subseteq R$ and $f: A \rightarrow B$ be defined by $f(x)=x^2-3x+2$. If $f$ is a bijection,then

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?

Let $f: R \rightarrow R$ be defined by $f(x) = \begin{cases} x + 2, & x \leq -1 \\ x^2, & -1 < x < 1 \\ 2 - x, & x \geq 1 \end{cases}$. Then the value of $f(-1.75) + f(0.5) + f(1.5)$ is