If $f(x) = (a - x^n)^{1/n},$ where $a > 0$ and $n$ is a positive integer,then $f[f(x)] = $

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) = $

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 $............$.

If $f(x) = \begin{cases} 2+2x, & -1 \leq x < 0 \\ 1-\frac{x}{3}, & 0 \leq x \leq 3 \end{cases}$ and $g(x) = \begin{cases} -x, & -3 \leq x \leq 0 \\ x, & 0 < x \leq 1 \end{cases}$,then the range of $(f \circ g)(x)$ is:

Give examples of two functions $f: N \rightarrow N$ and $g: N \rightarrow N$ such that $g \circ f$ is onto but $f$ is not onto.

$f: R \rightarrow R$ and $g:[0, \infty) \rightarrow R$ are defined by $f(x)=x^2$ and $g(x)=\sqrt{x}$. Which one of the following is not true?