All Tasks - Asymptote

The domain ($D_f$) of the function $f(x)= -3\pi + 2\arccos\left( \dfrac{1}{3x+1}\right)$ is:

Consider $f(x)= -3\pi +2 \arccos(3x+1)$ with domain $D_f=\left[ -\dfrac{2}{3}, 0\right]$ and range $D'_f = \left[ -3\pi, -\pi\right]$. The analytic expression of the inverse function of $f$, $f^{-1}(x)$, its domain ($D_{f^{-1}}$) and $f^{-1}(-\pi)$ are, respectively,

Consider the functions $f(x)= 5 \arccos\left(2x\right)$ with domain $D_f = \left[-\dfrac{1}{2}, \dfrac{1}{2}\right]$ and range $D'_f = \left[0, 5\pi\right]$ and $g(x)= \arccos\left(\dfrac{x}{2}\right)-3\pi$ with domain $D_g = \left[-2, 2\right]$ and range $D'_g = \left[-3\pi, -2\pi\right]$. State whether the following statements are true (T) or false (F).

Let $f(x)= -3\pi +2 \arccos\left( e^{3x+1}\right) $ with range $D'_f = \left[ -3\pi, -2\pi\right[$. Consider that $f^{-1}(x)$ is the analytic expression of the inverse function of $f$. State whether the following statements are true (T) or false (F).

Let $f(x)= -3\pi+2\arccos(3x+1)$ of domain $D_f=\left[-\dfrac{2}{3}, 0\right]$. The solution of inequality $f(x) > \arccos\left( -\dfrac{1}{2}\right) - 3 \arccos\left(-1\right)$ is:

Consider the functions $f(x)= 5 \arccos\left(2x\right)$ with domain $D_f=\left[-\dfrac{1}{2}, \dfrac{1}{2}\right]$ and $g(x)= \arccos\left(\dfrac{x}{2}\right)-3\pi$ with domain $D_g=\left[-2, 2\right]$. The solution of the equation $f(x) = 5 \ g(x)+15\pi$ is: