+8 \(\)
\(\) find the sum of all solutions to the equation
\([f(y) = \left\{ \begin{array}{cl} -y + 3 & \text{if } y \le 0, \\ 2y - 5 & \text{if } y > 0. \end{array} \right.\)
Find the sum of all solutions to the equation f(f(x))=4
Thanks for the help in advance!
+1005 f(f(x)) = 4 implies that f(x) must have been -1, or 4.5
This is since f(-1) = 4 and f(4.5) = 4
These are *probably* the only solutions
Onwards!
If the f(x) is -1, then it must mean that x = -4. -4 + 3 = -1. It cant be the solution from 2y-5 as it is negative.
for f(x) = 4.5, it is positive, so 2y-5 = 4.5
2y = 9.5
y = 4.75
Let's check our work.
f(f(-4)) = f(-4 +3) = f(-1) = -(-1) + 3 = 4!
f(f(4.75)) = f(9.5 -5) = f(4.5) = 9- 5 = 4
I am sure these are the only solutions
-4 + 4.75 = 0.75
If you don't understand anything feel free to ask!.
