Are the following statements true or false?

1. The set of all $x$'s that are in the domain of $g$ and where $g(x)$ is in the domain of $f$ correctly describes the domain of $f(g(x))$.

2. If $x$ is an element of the domain of $f(g(x))$, then $x$ is an element of the domain of $f(x)$.

3. For any relation $f$, it must be that $f( c \cdot x ) = c \cdot f( x )$ as long as $c$ is a constant.

4. If $x$ is in the domain of $\frac{f}{g}$, then $x$ is in the domain of $(f+g)(x)$.

5. If $f(x) = 5$, then $f( a + h ) = 5$.

6. $( f \cdot g )(a) = f(a) \cdot g(a)$ as long as $a$ is in both the domain of $f$ and in the domain of $g$.