Let $f: R \rightarrow R$ and $g: R \rightarrow R$ be defined by $f(x)=2x+1$ and $g(x)=x^2-2$. Determine $(g \circ f)(x)$.

$f: R - \left(-\frac{3}{5}\right) \rightarrow R$ is defined by $f(x) = \frac{3x-2}{5x+3}$,then $f \circ f(1)$ is

$f(x) = (20 - x^4)^{1/4}$ for $0 < x < \sqrt{5}$, then $f(f(1/2))$ is equal to

Let $f(x) = \frac{x+1}{x-1}$ for all $x \neq 1$. Let $f^1(x) = f(x)$,$f^2(x) = f(f(x))$ and generally $f^n(x) = f(f^{n-1}(x))$ for $n > 1$. Let $P = f^1(2) \cdot f^2(3) \cdot f^3(4) \cdot f^4(5)$. Which of the following is a multiple of $P$?

Let $g(x) = 1 + x - [x]$ and $f(x) = \begin{cases} -1, & \text{if } x < 0 \\ 0, & \text{if } x = 0 \\ 1, & \text{if } x > 0 \end{cases}$. Then for all values of $x$,the value of $f(g(x))$ is:

If $f(x) = \frac{1}{1 - x}$,then the derivative of the composite function $f[f\{ f(x)\} ]$ is equal to