Let
\(f(n) = \left\{ \begin{array}{cl} n^2-2 & \text{ if }n<0, \\ 2n-20 & \text{ if }n \geq 0. \end{array} \right.\)
What is the positive difference between the two values of \(a\) that satisfy the equation \(f(-2)+f(2)+f(a)=0\)?
f(-2) = (-2)^2 - 2 = 2
f (2) = 2(2) - 20 = -16
So
2 - 16 = - 14
So we need f(a) to = 14
Note that if a = -4 then f (a) = f (-4) = (-4)^2 - 2 = 14
And if a = 17 then 2(17) - 20 = 14
a = 17 or a = - 4
And their + difference = 21
