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Question

The function f(x) is continuous in the interval (a, b) then which among the following is true?


A

Function may or may not have a value at x=a,b

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B

Function should exist at x=a but may not be continuous

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C

f(a) = limxa+f(x)

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D

f(a) > f(b)

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Solution

The correct option is A

Function may or may not have a value at x=a,b


Its given that the function is continuous in (a, b). since a and b are excluded from the interval it can't be said for sure anything about the value of function at a and b .For the same reason we cant say anything about the continuity of function at these end points. Similarly the option (c) is true only when the point a is included in the interval or when it's a closed interval instead of an open interval.


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