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If f(x) be continuous function and g(x...

If f(x) be continuous function and g(x) be discontinuous, then

A

`f(x)+g(x)` must be continuous

B

`f(x)+g(x)` must be discontinuous

C

`f(x)=g(x)` for all x

D

Can't say

Text Solution

Verified by Experts

The correct Answer is:
B
If possible, suppose that f(x) + g(x) is continuous.
Now, `g(x)=[f(x)+g(x)] -f(x)`
Since, difference of two continuous functions is continuous, therefore g(x) is continuous, which is a contradiction.
Hence, f(x) + g(x) must be discontinuous.
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