The function $f(x) = \sec \left[ \log \left( x + \sqrt{1 + x^2} \right) \right]$ is . . . . . . function.

If $f(x)=3[x]+\{x+1\}$,where $[x]$ is the greatest integer function of $x$ and $\{x\}$ is the fractional part function of $x$,then $f(-1.32)=$

Let $S=(0,1) \cup(1,2) \cup(3,4)$ and $T=\{0,1,2,3\}$. Then which of the following statements is(are) true?
$(A)$ There are infinitely many functions from $S$ to $T$.
$(B)$ There are infinitely many strictly increasing functions from $S$ to $T$.
$(C)$ The number of continuous functions from $S$ to $T$ is at most $120$.
$(D)$ Every continuous function from $S$ to $T$ is differentiable.

Let $[x]$ denote the integral part of $x \in R$. Let $g(x) = x - [x]$. Let $f(x)$ be any continuous function with $f(0) = f(1)$. Then the function $h(x) = f(g(x))$:

Let $f: R \to R$ be a function. Define $g: R \to R$ by $g(x) = |f(x)|$ for all $x$. Then $g$ is

The total number of functions $f: \{1, 2, 3, 4\} \to \{1, 2, 3, 4, 5, 6\}$ such that $f(1) + f(2) = f(3)$ is equal to: