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Let \(f(x) = \left\{ \begin{array}{cl} 2x + 7 & \text{if } x < -2, \\ -x^2 - x + 1 & \text{if } x \ge -2. \end{array} \right.\)Find the sum of all values of x such that f(x)=-5.

 Aug 28, 2018
 #1
avatar+98125 
+1

2x + 7  = -5      

2x  = -12

x = -6

 

-x^2 - x + 1    = -5     multiply through by -1

x^2 + x - 1  = 5

x^2 + x  - 6  = 0   factor

(x + 3) ( x - 2)  =  0

Set each factor to  0  and solve for  x and we get   x  = -3   (out of the domain for the function)  or  x = 2

 

So...the sum of the  x values such that f(x)   = -5  ⇒   -6  + 2   =  -4 

 

cool cool cool

 Aug 28, 2018

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