+865 Suppose that a and b are positive real numbers, and let \( f(x) = \begin{cases} \frac{a}{b}x & \text{ if }x\le-4, \\ abx^2 & \text{ if }x>-4. \end{cases} \)if \(f(-4)=-\frac{60}{13} and f(4)=3120\), what is a+b?
+23252 Since f(-4) = -60/13
and f(-4) = (a/b)x,
then a possibility is: f(-4) = (15/13)(-4) ---> a = 15 and b = 13
[other possibilities are multiples of (15/13)]
Let's see what happens with f(4) ---> f(4) = a·b·(4)2 = (15)·(13)·42 = 3120.
Since this checks out, a = 15 and b = 13.
