If $f(x) = 3x + 10$ and $g(x) = x^2 - 1$,then $(fog)^{-1}(x) = $

If $f : R \to R$ and $g : R \to R$ are defined as $f(x) = 2x - |x|$ and $g(x) = 2x + |x|$, then

Let $f(x) = \frac{ax + b}{cx + d}$. Then,$f \circ f(x) = x$ provided that

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 .... .

For a suitably chosen real constant $a$,let the function $f: R-\{-a\} \rightarrow R$ be defined by $f(x)=\frac{a-x}{a+x}$. Further,suppose that for any real number $x \neq-a$ and $f(x) \neq-a$,$(f \circ f)(x)=x$. Then,$f\left(-\frac{1}{2}\right)$ is equal to

If $f(x) = x^2$ and $g(x) = [x^2]$, where $[ \cdot ]$ represents the greatest integer function, then $(f \circ g)(\frac{3}{2}) + (g \circ f)(\frac{3}{2})$ is equal to ...