Question

# Assertion :$$f(x)=\sin x+[x]$$ is discontinuous at $$x=0$$ because Reason: If $$g(x)$$ is continuous and $$h(x)$$ is discontinuous at $$x=a$$, then $$g(x)+h(x)$$ will necessarily be discontinuous at $$x=a$$

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C
Assertion is correct but Reason is incorrect
D
Assertion is incorrect but Reason is correct

Solution

## The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for AssertionAt $$x=0$$, $$\sin x$$ is continuous but $$[x]$$ is not continuous.Hence $$f(x) = \sin x+[x]$$ is discontinuous at $$x=0$$Thus both statement are correct and Assertion is followed by Reason.Mathematics

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