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
• B. Function should exist at x=a but may not be continuous
• C. f(a) = $\underset{x\to a^{+}}{lim}f\left(x\right)$
• D. f(a) > f(b)

Answer 1

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.