If f.g is continuous at x = a, then f and g are separately continuous at x = a. - Mathematics

प्रश्न

If f.g is continuous at x = a, then f and g are separately continuous at x = a.

पर्याय

True
False

MCQ

चूक किंवा बरोबर

उत्तर

This statement is False.

Explanation:

Let us take an example: f(x) = sin x and g(x) = cot x

∴ f(x).g(x) = sinx . cotx

= $\sin x \cdot \frac{\cos x}{\sin x}$

= = cos x

Which is continuous at x = 0 but cot x is not continuous at x = 0.

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Algebra of Continuous Functions

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

Q 106 Q 105 Next

पाठ 5: Continuity And Differentiability - Exercise [पृष्ठ ११६]

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एनसीईआरटी एक्झांप्लर Mathematics [English] Class 12

पाठ 5 Continuity And Differentiability
Exercise | Q 106 | पृष्ठ ११६

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If f.g is continuous at x = a, then f and g are separately continuous at x = a. - Mathematics

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If f.g is continuous at x = a, then f and g are separately continuous at x = a. - Mathematics

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