Question

What are the removable discontinuities of the following function? f (x) = startfraction x squared minus 36 over x cubed minus 36 x endfraction x = –6, x = 0, and x = 6 x = –6 and x = 6 x = 0 and x = –6 x = 0 and x = 6

Answer 1

The removable discontinuity is at negative 6 and 6. Then the correct option is B.

What is a function?

The function is an expression, rule, or law that defines the relationship between one variable to another variable. Functions are ubiquitous in mathematics and are essential for formulating physical relationships.

The function is given as

$f\rm (x) =\rm \dfrac{x^2-36}{x^3-36x}$

The expression can be written as

$f\rm (x) =\rm \dfrac{x^2-36}{x(x^2-36)}$

$f\rm (x) = \dfrac{1}{x}$

The non-removable discontinuity is x = 0.

More about the function link is given below.

brainly.com/question/5245372