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.
+128475 We have that
2x + 7 = -5 subtract 7 from both sides or -x^2 - x + 1 = -5
2x = -12 divide both sides by 2 rearrange as
x = - 6 x^2 + x - 6 = 0
factor
(x + 3) ( x - 2) = 0
Set each factor to 0 and solve for x
x = -3 x = 2
Only x = 2 is defined for the function
The sum of the x values =
-6 + 2
-4
