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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: $$\begin{align*} f(x) &= \begin{cases} x^2 + 1 & \text{if } x \in (-\infty, 0) \\ x - 2 & \text{if } x \in [0, +\infty) \end{cases} \\ g(x) &= \begin{cases} x + 2 & \text{if } x \in (-\infty, 2) \\ 1 - 2x^2 & \text{if } x \in [2, +\infty) \end{cases}. \end{align*}$$

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  • $\begingroup$ You should provide a picture with better quality or rewrite a problem, also show what you have already tried. $\endgroup$
    – whiskeyo
    Feb 6, 2019 at 20:42
  • $\begingroup$ Redefine your functions on 3 intervals :$(-\infty,0)$, $(0,2)$, $(2,\infty)$ and compose your functions over these intervals. $\endgroup$ Feb 6, 2019 at 20:42
  • $\begingroup$ link italic bold code this my attempt and task $\endgroup$ Feb 6, 2019 at 20:44

1 Answer 1

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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 $x\ge 0$.

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