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Question

Let $$f(x)$$ be a continuous function and $$g(x)$$ be a discontinuous function, then$$f(x) + g(x)$$ is discontinuous function.


A
True
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B
False
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Solution

The correct option is A True
If $$f$$ is continuous and $$h$$ is continuous then $$g=h−f$$ is continuous.
So if $$f$$ is continuous and $$g$$ is discontinuous $$f+g=h$$ can not be continuous else $$h−f=g$$ would also be continuous.
Hence if $$f(x)$$ be a continuous function and $$g(x)$$ be a discontinuous function, then $$f(x)+g(x)$$ is discontinuous function.

Mathematics

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