examine the continuity of the function f(x)=1 divided by x+3, x belongs to R.

Asked by Rashmi gondi | 21st Dec, 2013, 07:00: PM

Expert Answer:

The given function is
A function is continuous if it is defined at all points in the domain of the function.
Defined means a finite value.
f(x) will not be defined, that is, will have an infinte value at x = -3
As, at x = -3, the value of
At no other point, this occurs.
Thus, the function
is continuous at all points except at x=-3.
It can also be solved using the concept of limits.
Left Hand Limit = Right Hand Limit = Finite Value
is the condition for continuity.
Examine the function's point of possible discontinuity.
Similarly calculate the RHL. It will also give infinity. Since the limit is not finite, the limit does not exist at x = -3. Thus, the function is discontinuous at x = -3.

Answered by Vimala Ramamurthy | 22nd Dec, 2013, 12:50: PM

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