If $f(x) = ax + b$ and $g(x) = cx + d$,then $f(g(x)) = g(f(x))$ is equivalent to

If $f(x) = \sin^2 x$ and the composite function $g(f(x)) = |\sin x|$,then the function $g(x)$ is equal to

For $x \in \left( 0, \frac{3}{2} \right)$,let $f(x) = \sqrt{x}$,$g(x) = \tan x$,and $h(x) = \frac{1 - x^2}{1 + x^2}$. If $\phi(x) = ((h \circ f) \circ g)(x)$,then $\phi\left( \frac{\pi}{3} \right)$ is equal to

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are two functions defined by $f(x) = ax + b$ $(a \neq 0)$ for all $x \in R$ and $g(x) = cx^3 + d$ $(c \neq 0)$ for all $x \in R$,then $(f \circ g)^{-1}(x) =$

If $f(x)=\sqrt{x}$ $(x \geq 0)$ and $g(x)=1+x^2$, then $(f \circ g)^{\prime}(1)=$

Let $f(x) = x^3$ and $g(x) = 3^x$,then the quadratic equation whose roots are solutions of the equation $(f \circ g)(x) = (g \circ f)(x)$ (for $x \neq 0$) is