Answer:
D
Step-by-step explanation:
We have the piecewise function: 

And we want to find x such that f(x)=1. 
So, let's substitute 1 for f(x): 

This has two equations. So, we can separate them into two separate cases. Namely: 

Let's solve for x in each case. 
Case I: 
We have: 

Add 1 to both sides: 

Let's cancel out the fraction by multiplying both sides by -2. So: 

The right side cancels: 

Flip: 

So, x is -4. 
Case II: 
We have: 

Flip: 

This is the solution for our second case. 
So, we have: 

Now, can check to see if we have to to remove solution(s) that don't work. 
Note that x=-4 is the solution to our first equation. 
The first equation is defined only if x is less than -2. 
-4 <em>is </em>less than -2. So, x=-4 is indeed a solution. 
x=1 is the solution to our second equation. 
The second equation is defined only if x is greater than or equal to -2. 
1 <em>is</em> greater than or equal to -2. So, x=1 is <em>also </em>a solution. 
Therefore, our two solutions are: 

Out of our answer choices, we can pick D. 
And we're done!