Piecewise Functions

0  =  -x - 3

                      Add  x  to both sides of the equation.

x  =  -3

 

-3  is  ≤  1  so  -3  is a solution to  f(x) = 0

 

0  =  x/2 + 1

                      Subtract  1  from both sides.

-1  =  x/2

                      Multiply both sides by  2 .

-2  =  x

 

-2  is not  >  1  so  -2  is not a solution to  f(x)  =  0

 

The only value of  x  that makes  f(x) = 0  is  -3

 

So the sum of all values of  x  such that  f(x) = 0  is just  -3 .