$f(x)=\frac{x}{e^x-1}+\frac{x}{2}+2 \cos ^3 \frac{x}{2}$ on $R-\{0\}$ is

The function $f: R \rightarrow R$ defined by $f(x) = e^x + e^{-x}$ is

Let $f : R \rightarrow R$ be a function such that $f(x) = \frac{x^2+2x+1}{x^2+1}$. Then

If $f(x) = \begin{cases} [x], & -3 < x \leq -1 \\ |x|, & -1 < x < 1 \\ |[x]|, & 1 \leq x < 3 \end{cases}$ then the set $\{x : f(x) \geq 0\}$ is equal to

Let $A = \{x : x \in R, x \text{ is not a positive integer}\}$. Define $f: A \rightarrow R$ as $f(x) = \frac{2x}{x-1}$. Then $f$ is:

$A = \{1, 2, 3, 4\}$ and $B = \{1, 2, 3, 4, 5, 6\}$ are two sets, and the function $f: A \rightarrow B$ is defined by $f(x) = x + 2$ for all $x \in A$. Then the function $f$ is: