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Are the following statements true or false?

1. If $f$ and $h$ are reciprocal relations, then the domain of $h$ is a subset of the domain of $f$ .

2. $f^{-1} (x) = \frac{1}{f(x)}$ for any relation $f$ .

3. Given two relations $f$ and $g$ , then $f(g(x)) = g(f(x))$ only if $f$ and $g$ are inverses of each other.

4. Given two relations $f$ and $g$ , then $f(g(x)) = g(f(x))$ only if $f$ and $g$ are inverses of each other and both are nicely defined at $x$ .

5. If $f$ and $h$ are reciprocal relations, then the domain of $f$ is equal to the domain of $h$ .

You can earn 60% partial credit for 3 correct answers, and 80% partial credit for 4 correct answers.