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

Let $f(x)=x^2$ and $g(x)=\sin x$ for all $x \in R$. Then the set of all $x$ satisfying $(f \circ g \circ g \circ f)(x)=(g \circ g \circ f)(x)$,where $(f \circ g)(x)=f(g(x))$,is

If $g(x) = x^2 + x - 2$ and $(g \circ f)(x) = 2x^2 - 5x + 2$, then $f(x)$ is equal to

If $f(x) = |\cos x|$ and $g(x) = [x]$,then $gof(x)$ is equal to

If $f: R \rightarrow R$ is defined by $f(x)= \begin{cases} |[x-5]|, & \text{for } x < 5 \\ [|x-5|], & \text{for } x \geq 5 \end{cases}$ Then,$(f \circ f)\left(-\frac{7}{2}\right) = ?$ (here,$[x]$ is the greatest integer function)

If $\phi(x) = x^2 + 1$ and $\psi(x) = 3^x$,then find $\phi \{ \psi(x) \}$ and $\psi \{ \phi(x) \}$.