+0

# Piecewise-Defined Functions

+1
92
1
+193

Let

$p(x,y) = \begin{cases} x + y &\quad \text{if } x \ge 0 \text{ and } y \ge 0, \\ x - 2y &\quad \text{if } x < 0 \text{ and } y < 0, \\ 3x + y &\quad \text{otherwise}. \end{cases}$

What is $p(p(1,-1),p(-5,-2))$?

Feb 12, 2021

#1
+86
+4

@above, simply functional evaluation. For p(1,-1), then the case is 'otherwise' so we have 3*1-1=2. For p(-5,-2) we have case 2, so then -5-2(-2) equals -1. The outer function then has arguments 2 and -1, which is in the case 'otherwise' so we have 6-1=5.

So the final functional output is 5.

Feb 13, 2021