+0

0
40
2
+109

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

Aug 24, 2020

#1
0

The sum of all values of x is 2 + 12 = 14.

Aug 24, 2020
#2
+109
-1

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

dp1806  Aug 24, 2020