##### The following function is

The following function is ____________ at x = 3 and ____________ x = −3.

(A) Continuous, Continuous

(B) Not Continuous, Undefined

(C) Continuous, Not Continuous

(D) Not Continuous, Continuous

Answer: C

Discuss

The following function is ____________ at x = 3 and ____________ x = −3.

(A) Continuous, Continuous

(B) Not Continuous, Undefined

(C) Continuous, Not Continuous

(D) Not Continuous, Continuous

Answer: C

Discuss

On evaluation of left hand and right hand limits , they both come to be same at both x= 3 and x = -3 which is equal to 9/2.

But for continuity , LHL = RHL = value of function at that point.

So at x = 3 we have f(x) = 9/2.But not such value given at x = -3.

Hence function is continuous at x = 3 and discontinuous at x = -3.

Hence C is the correct option.

why the function is discontinuous at x=-3, when we have LHL=RHL=value of function=MINUS INFINITY, at x=-3 the function is (x^3-27)/(x^2-9).

@vikash957 at x= -3, function is not defind ( devide by zero).