If $f$ is the greatest integer function and $g$ is the modulus function,then $(gof)\left( -\frac{5}{3} \right) - (fog)\left( -\frac{5}{3} \right) = $

If $f: R \rightarrow R$ is defined by $f(x)=e^{x}$ and $g: R \rightarrow R$ is defined by $g(x)=x^{2}$, then the mapping $(g \circ f): R \rightarrow R$ is defined by $(g \circ f)(x) = g(f(x))$ for all $x \in R$. Which of the following is true?

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 the function is $f(x)=\frac{1}{x+2}$,then the point of discontinuity of the composite function $y=f(f(x))$ is

Let $f: R \rightarrow R$ be defined as $f(x)=x-1$ and $g: R -\{1,-1\} \rightarrow R$ be defined as $g(x)=\frac{x^{2}}{x^{2}-1}$. Then the function $f \circ g$ is

If $f(x) = x^2 + 1$,then $fof(x)$ is equal to