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

 Aug 24, 2020
 #2
avatar+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

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