The relation $R$ is defined as $R = \{(4, 5), (1, 4), (4, 6), (7, 6), (3, 7)\}$. Then $R^{-1} o R$ is:

Let $f(x) = \sin^{-1} x$ and $g(x) = \frac{x^2 - x - 2}{2x^2 - x - 6}$. If $g(2) = \lim_{x \to 2} g(x)$,then the domain of the function $f \circ g$ is .... .

If $f(x) = \frac{4x+3}{6x-4}$,$x \neq \frac{2}{3}$ and $(f \circ f)(x) = g(x)$,where $g: R - \{\frac{2}{3}\} \rightarrow R - \{\frac{2}{3}\}$,then $(g \circ g \circ g)(4)$ is equal to

If $g(x)=x^2+x-1$ and $(g \circ f)(x)=4 x^2-10 x+5$,then $f(2)$ is equal to

If $f(x) = \frac{2x+3}{3x-2}$,$x \neq \frac{2}{3}$,then $(f \circ f)(x)$ is:

Let $N$ denote the set of all natural numbers,and $Z$ denote the set of all integers. Consider the functions $f: N \rightarrow Z$ and $g: Z \rightarrow N$ defined by $f(n) = \begin{cases} (n+1)/2 & \text{if } n \text{ is odd} \\ (4-n)/2 & \text{if } n \text{ is even} \end{cases}$ and $g(n) = \begin{cases} 3+2n & \text{if } n \geq 0 \\ -2n & \text{if } n < 0 \end{cases}$. Define $(g \circ f)(n) = g(f(n))$ for all $n \in N$,and $(f \circ g)(n) = f(g(n))$ for all $n \in Z$. Then which of the following statements is (are) True?