+0  
 
+2
50
4
avatar+59 

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

 Mar 24, 2021

Best Answer 

 #1
avatar+721 
+6

grinding some piecewise-defined functions today, aren't we?

 

we have $2x + 7 = -5$, so $x = -6.$

 

we also have $-x^2 - x + 1 = -5$, and solving for $x$ gives us solutions of $-3$ and $2.$ As $-3$ is not greater or equal than $-2$, we only consider the $2.$

 

So, the values of $x$ are $-6$ and $2.$ the sum of these is $\boxed{-4}.$ nice

 Mar 24, 2021
 #1
avatar+721 
+6
Best Answer

grinding some piecewise-defined functions today, aren't we?

 

we have $2x + 7 = -5$, so $x = -6.$

 

we also have $-x^2 - x + 1 = -5$, and solving for $x$ gives us solutions of $-3$ and $2.$ As $-3$ is not greater or equal than $-2$, we only consider the $2.$

 

So, the values of $x$ are $-6$ and $2.$ the sum of these is $\boxed{-4}.$ nice

CentsLord Mar 24, 2021
 #2
avatar+59 
0

D**n, I hate it when I get exposed

 Mar 24, 2021
 #3
avatar+721 
+4

though, piecewise defined functions are very good for rating so grind on

 Mar 24, 2021
 #4
avatar+59 
+1

BAHAHAHA

 Mar 24, 2021

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