If $f(x) = 8x^3$ and $g(x) = x^{1/3}$,then $f \circ g(x)$ is:

Let $f, g$ and $h$ be functions from $R$ to $R$. Show that:
$\begin{cases} (f+g)oh = foh + goh \\ (f \cdot g)oh = (foh) \cdot (goh) \end{cases}$

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x) = x^{2} - 3x + 4$ and $g(x) = 2x + 1$,then the value of $x$ for which $f(x) = (f \circ g)(x)$ is

Let $f: R - \left\{-\frac{1}{2}\right\} \rightarrow R$ be defined by $f(x) = \frac{x-2}{2x+1}$. If $\alpha$ and $\beta$ satisfy the equation $f(f(x)) = -x$,then $4(\alpha^2 + \beta^2) = $

Let $f$ and $g$ be two functions defined by $f(x) = \begin{cases} x+1, & x < 0 \\ |x-1|, & x \geq 0 \end{cases}$ and $g(x) = \begin{cases} x+1, & x < 0 \\ 1, & x \geq 0 \end{cases}$. Then $(g \circ f)(x)$ is

If $f(x)=e^{|x|}$ and $g(x)=\log x$,then $(g \circ f)(x) =$