All Tasks - Asymptote

Simplfy the following expression: $A=(x-2)^2-x^2$ and then identify the correct statements

Simplfy the following expression: $\frac{{(2x-3)}^2-4(x-2)(x+2)+x(x^2+15)-25}{x^2+3}$ and then identify the correct statements

Simplfy the following expression: $A=(x-y)^2-(x^2+4)$ and then identify the correct statements

Consider $f(x)= \dfrac{\pi}{2} -2 \arctan(1-2x)$ with domain $D_f=\mathbb{R}$ 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,

Let $f(x)= a +2 \arccos(3x+b)$, with $a, b \in \mathbb R$. Knowing that the domain and range of $f$ are, respectively, $D_f=\left[ -\dfrac{2}{3}, 0\right]$ and $D'_f=\left[ -3\pi, -\pi\right]$, then $a $ and $b$ are:

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