If $f(x) = x^3 - x$ and $g(x) = \sin^2 x$,then $f\left(g\left(\frac{\pi}{6}\right)\right) = $

For every real number $x \neq -1$,let $f(x) = \frac{x}{x+1}$. Define $f_1(x) = f(x)$ and for $n \geq 2$,$f_n(x) = f(f_{n-1}(x))$. Then the product $f_1(-2) \cdot f_2(-2) \cdot \ldots \cdot f_n(-2)$ is equal to:

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

If $f$ is the greatest integer function defined on $R$ as $f(x) = [x]$ and $g$ is the modulus function defined on $R$ as $g(x) = |x|$,then the value of $(g \circ f)\left(\frac{-5}{3}\right)$ is

If $f(x) = \log \left(\frac{1+x}{1-x}\right)$ and $g(x) = \frac{3x+x^3}{1+3x^2}$,then $(fog)(x) =$

Let $f : R \rightarrow R$ and $g : R \rightarrow R$ be defined as $f(x) = \begin{cases} x+a, & x < 0 \\ |x-1|, & x \geq 0 \end{cases}$ and $g(x) = \begin{cases} x+1, & x < 0 \\ (x-1)^2+b, & x \geq 0 \end{cases}$ where $a, b$ are non-negative real numbers. If $(g \circ f)(x)$ is continuous for all $x \in R$,then $a+b$ is equal to ......