\(\)

\(\) 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!

merrrrrr22 Jun 9, 2020

#3**+1 **

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!.

hugomimihu Jun 12, 2020