Let $f(x) = \frac{g(x)}{h(x)}$,where $g$ and $h$ are continuous functions on the open interval $(a, b)$. Which of the following statements is true for $a < x < b$?
- A$f$ is continuous at all $x$ for which $x$ is not zero.
- B$f$ is continuous at all $x$ for which $g(x) = 0$.
- C$f$ is continuous at all $x$ for which $g(x) \neq 0$.
- D$f$ is continuous at all $x$ for which $h(x) \neq 0$.
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