+108 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
+108 the answer is not 14 Mr. guest. You just picked two random numbers and used those as the answer. The correct answer is below:
We solve the equation \(f(x) = 0\) on the domains \(x \le 3 and x > 3.\)
If \(x \le 3, \) then \(f(x) = 2x + 1,\) so we want to solve \(2x + 1 = 0.\) The solution is \(x = -1/2,\) which satisfies \(x \le 3.\)
If \(x > 3,\) then \(f(x) = 8 - 4x,\) so we want to solve \(8 - 4x = 0.\) The solution is \(x = 2,\) but this value does not satisfy \(x > 3.\)
Therefore, the only solution is -1/2
