If a real-valued function $f$ is defined by $f(x) = \frac{ax + \sqrt{a^2 - x^2}}{bx}$,then $f$ is

The function $f:[0, \infty) \rightarrow [0, \infty)$ defined by $f(x) = \frac{x}{1+x}$ is

If $f : R \rightarrow R$ such that $f(x) = 5x - 3\cos x - 4\sin x$,then the function $f(x)$ is

For each $n \in N$, let $A_n = \{(n+1)k \mid k \in N\}$ and $X = \bigcup_{n \in N} A_n$. $A$ mapping $f: X \rightarrow N$ defined by $f(x) = x, \forall x \in X$, is

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.

Show that $f: N \rightarrow N$,given by $f(x) = \begin{cases} x+1, & \text{if } x \text{ is odd} \\ x-1, & \text{if } x \text{ is even} \end{cases}$ is both one-one and onto.