Maths · Limits, continuity and differentiability
If \) and \) are both continuous at then which of the following is/are always co
If \( f(x) \) and \( g(x) \) are both continuous at \( x=c \) then which of the following is/are always continuous at \( x=c ? \) This question has multiple correct options
- A. \( f(x)+g(x) \)
- B. \( (f(x)-g(x)) \times f(x) \)
- C. \( g(x) \times f(x) \)
- D. \( \frac{f(x)-g(x)}{g(x)} \)
Step-by-step solution
Since f and g are continuous at x=c, their sum is also continuous at that point by the limit laws for continuity. Options B and C are also always continuous because products of continuous functions are continuous. Option D is not always continuous as it may be undefined if g(c)=0.
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