## Find Direct/Inverse Images

1. The problem statement, all variables and given/known data

The problem is attached and my attempt for direct image is also attached.
I seek help in inverse image.

2. Relevant equations

3. The attempt at a solution
Attached Thumbnails

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 You did part (a) correctly! Part (b): If $$h = g \circ f,$$ then $$h^{-1} = f^{-1} \circ g^{-1}.$$ Look at the boundaries of G. They will give you the boundaries of its inverse image. This isn't ALWAYS the case, but our function here is pretty simple so it will work out well.
 Based on your suggestions... Attached Thumbnails

## Find Direct/Inverse Images

mhmm! and a nice self-assuring way to check that you "almost definitely" got it right is the fact that $$f(\{x : -2 \le x \le 0\}) = G.$$ I say "almost definitely" because it could happen that you luck out and it works even though your answer's wrong...but let's not worry about that haha. you got it right!
 It turns out, I am not too dumb, yay!! (Thank you for your patience, Raskolnikov.)