4. Let f(x) = 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?
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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) is not equal to zero. |
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D. f is continuous at all x for which h(x) is not equal to zero. |
E. f is possibly discontinuous even though h(x) is not equal to zero. |
Solution: The answer is D
By theorem, if g and h are continuous functions on the open interval (a,b), then g/h is also continuous at all x in the open interval (a,b) where h(x) is not equal to zero.