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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View SolutionLet $[t]$ denote the greatest integer less than or equal to $t$. Let $f:[0, \infty) \rightarrow \mathbb{R}$ be a function defined by $f(x) = [\frac{x}{2} + 3] - [\sqrt{x}]$. Let $S$ be the set of all points in the interval $[0, 8]$ at which $f$ is not continuous. Then $\sum_{a \in S} a$ is equal to:
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