I know how to compose normal functions but never seen this type of task any help?
Find the composition $g \circ f$ of the following functions $f, g : \Bbb{R} \to \Bbb{R}$ given by the formulas: $$\begin{align*} f(x) &= \begin{cases} x^2 + 1 & \text{if } x \in (-\infty, 0) \\ x - 2 & \text{if } x \in [0, +\infty) \end{cases} \\ g(x) &= \begin{cases} x + 2 & \text{if } x \in (-\infty, 2) \\ 1 - 2x^2 & \text{if } x \in [2, +\infty) \end{cases}. \end{align*}$$
Hint:
To calculate $g\bigl(f(x)\bigr)$, you have to determine when $f(x)<2$ and when $f(x)\ge 2$. Consider separately the cases $x<0$ and $x\ge 0$.