WeBWorK Standalone Renderer

Are the following statements true or false?

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

2. If $x$ is in the domain of $g$ , then $x$ is in the domain of $( f + g )(x)$ .

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. The domains of $(f + g)(x)$ , $(f - g)(x)$ and $(f \cdot g)(x)$ are all the same.

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

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

You can earn 30% partial credit for 2 - 3 correct answers, and 60% partial credit for 4 - 5 correct answers.