Let $f(x) = \displaystyle x+2$ and $g(x)= \displaystyle \frac{1}{x+2}.$ Find the following compositions.

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1. $(f \circ f)(x) =$

2. $(f \circ g)(x) =$

3. $(g \circ f)(x) =$

4. $(g \circ g)(x) =$

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