The number of non-constant functions $f: X \to Y$ where $X = \{0, 1, 2\}$ and $Y = \{1, 2, 3, 4, 5, 6, 7, 8\}$ such that $f(i) \leq f(j)$ whenever $i < j$ is:

The function $y = \frac{2x - 1}{x - 2}$ $(x \neq 2)$:

Let $A = \{1, 2, 3, \ldots, 10\}$ and $f: A \rightarrow A$ be defined as $f(k) = \begin{cases} k + 1 & \text{if } k \text{ is odd} \\ k & \text{if } k \text{ is even} \end{cases}$. Then the number of possible functions $g: A \rightarrow A$ such that $g \circ f = f$ is ...... .

If $f : R \rightarrow R$ is defined by $f(x) = \begin{cases} x + 4, & x < -4 \\ 3x + 2, & -4 \leq x < 4 \\ x - 4, & x \geq 4 \end{cases}$ then the correct matching of List-$I$ from List-$II$ is :
List-$I$
$(A) f(-5) + f(-4)$
$(B) f(|f(-8)|)$
$(C) f(f(-7) + f(3))$
$(D) f(f(f(f(0)))) + 1$
List-$II$
$(i) 14$
$(ii) 4$
$(iii) -11$
$(iv) -1$
$(v) 1$
$(vi) 0$

Let $f:[0,1] \rightarrow \mathbb{R}$ be an injective continuous function that satisfies the condition $-1 < f(0) < f(1) < 1$. Then,the number of functions $g:[-1,1] \rightarrow [0,1]$ such that $(g \circ f)(x) = x$ for all $x \in [0,1]$ is

Let $f(x) = \frac{\sqrt{x - 2\sqrt{x - 1}}}{\sqrt{x - 1} - 1}$. Then: