Question

Explain why f(x)= 1/(x-x3)^3 is not continuous at x = 3.

Answer 1

Answer: Option b.

Explanation:

1. You have the function
`f(x)=(1)/((x-3)^(3))` given in the problem above.

2. You must keep on mind that. by definition, the division by zero does not exist.

3. The value x=3 makes the denominator of the function f(x) equal to zero. Therefore you can conclude that the function shown in the problem is not defined at x=3.

The answer is the option b.

Answer 2

Choice B is correct.

Explanation:

We have given a function:

f(x)=1/(x-3)³

We have to explain that function is not continuous at x=3.

The domain is all possible values of x for which the function is defined.

When we put x=3 in the function, the denominator of function is zero.

f(x)=1/(x-3)³ = 1/(3-3)³ =1/0= undefined

Function is undefined when it contain 0 in its denominator.

That is why function is not continuous at x=3.

Choice B is correct.