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Let $f(x) = \left\{ \begin{array}{cl} 2x + 1 & \text{if } x \le 3, \\ 8 - 4x & \text{if } x > 3. \end{array} \right.$Find the sum of all values of $x$ such that $f(x) = 0.$

Guest Sep 1, 2017
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$$Let $f(x) = \left\{ \begin{array}{cl} 2x + 1 & \text{if } x \le 3, \\ 8 - 4x & \text{if } x > 3. \end{array} \right.$Find the sum of all values of x such that f(x) = 0.$$

2x + 1  = 0

2x  = -1

x = - 1/2     and this is in the domain  of x ≤ 3

8 - 4x = 0

8 = 4x

2 = x       this is not in the domain of x > 3

So......the sum is just -1/2

CPhill  Sep 1, 2017