Let \(f(x) = \begin{cases} 9x+16 &\text{if }x<2, \\ 2x-14&\text{if }x\ge2. \end{cases} \)If f(x)=-2, find the sum of all possible values of x.
Please help me, how am I supposed to proceed with this?
+23246 Since f(x) = 2, there are two ways that the answer is 2.
First way: if x < 2: 9x + 16 = 2 ---> 9x = -14 ---> x = -14/9.
Second way: if x >= 2: 2x - 14 = 2 ---> 2x = 16 ---> x = 8
You will now need to add the two possible values for x ...
Oh, so what I do is just plug in the value -2 for 9x+16 and 2x-14?
By the way, there's a mistake because f(x)= -2, not 2.
+23246 Thanks -- I read it as 2, not -2:
First: 9x + 16 = -2 ---> 9x = -18 ---> x = -2
Second: 2x - 14 = -2 ---> 2x = 12 ---> x = 6
To "find the sum of all possible values of x"
-- there are only two ways; either x = -2 or x = 6
So, to find the sum, the answer is: -2 + 6 = 4.
