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Let \mathrm{ 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 \mathrm{ a<x<b } ?

Option: 1

\mathrm{ f(x) \text { is continuous at all } x \text { for which } x \text { is not zero. }}


Option: 2

\mathrm{ f(x) \text { is continuous at all } x \text { for which } g(x)=0 \text {. } }


Option: 3

\mathrm{f(x) \text { is continuous at all } x \text { for which } g(x) \neq 0 }


Option: 4

\mathrm{ f(x) is\, \, continuous \, \, at\, \, all\, \, x \, \, \, for\, \, which\, \, h(x) \, \, is \, \, not \, \, equal\, \, to \, \, zero. }


Answers (1)

best_answer

\mathrm{f(x)=\frac{g(x)}{h(x)} }By theorem, if g and hare contunous function on die open interval (a, b) then \mathrm{\frac{g}{h} } is alse contunuous at all x in the open interval (a, b) where h(1) is not equal to zero

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seema garhwal

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