All Tasks - Asymptote

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

The domain ($D_f$) and the range ($D'_f$) of function $f(x)= 2 \left|-\pi + \arcsin(1-2x)\right| $ are, respectively,

Applying the chain rule, calculate $\frac{dy}{dx}(1)$ where $y(v)=arccot\left(v^2+v\right)$, and $v(u)=\ln(u^2-3)$, and $u(x)=\dfrac{x+1}{x}$

For each given tower, calculate the number of side faces visible side faces.

The depicted sequence of matchstick figures is continued. Give the term that can be used to determine the number of matches needed at the step n.

The depicted sequence of matchstick figures is continued. Indicate how many matchsticks are needed for step 4.