If $f(x) = \log_a x$ and $F(x) = a^x$,then $F[f(x)]$ is

Let $f(x) = \frac{x-1}{x+1}$,$x \in R - \{-1, 0, 1\}$. If $f^{n+1}(x) = f(f^n(x))$ for all $n \in N$,then $f^6(6) + f^7(7) = $

If $f(x) = \frac{3x+4}{5x-7}, x \neq \frac{7}{5}$ and $g(x) = \frac{7x+4}{5x-3}, x \neq \frac{3}{5}$,then $(g \circ f)(3) = $

Let the functions $f: R \rightarrow R$ and $g: R \rightarrow R$ be defined as $f(x) = \begin{cases} x+2, & x < 0 \\ x^2, & x \geq 0 \end{cases}$ and $g(x) = \begin{cases} x^3, & x < 1 \\ 3x-2, & x \geq 1 \end{cases}$. Then,the number of points in $R$ where $(f \circ g)(x)$ is $NOT$ differentiable is equal to

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

Let $f^1(x) = \frac{3x + 2}{2x + 3}$,$x \in R - \left\{-\frac{3}{2}\right\}$. For $n \geq 2$,define $f^n(x) = f^1 \circ f^{n-1}(x)$. If $f^5(x) = \frac{ax + b}{bx + a}$ and $\gcd(a, b) = 1$,then $a + b$ is equal to $............$.