Let $f(x) = \sin\!\left(7x\right)$ and $g(x)= \displaystyle \frac{x}{2+x}.$ Find $f \circ g,$ $g \circ f,$ $f \circ f,$ and $g \circ g$, and their respective domains.

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1. $f \circ g =$

2. What is the domain of $f \circ g$ ?
Answer (in interval notation):

3. $g \circ f =$

4. What is the domain of $g \circ f$ ?
Answer (in interval notation):

5. $f \circ f =$

6. What is the domain of $f \circ f$ ?
Answer in interval notation):

7. $g \circ g =$

8. What is the domain of $g \circ g$ ?
Answer (in interval notation):

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