Question

What are the discontinuities of the function f(x) = the quantity x squared minus 36 over the quantity 4x minus 24?

Answer 1

x^2 - 36

-----------    = (x - 6)(x + 6) /  4(x - 6)

4x - 24

When x =  6 the denominator = 0  so the discontinuity is x = 6.

Answer 2

Answer:

Discontinuities of the function is x = 6  .

Step-by-step explanation:

Given : f(x) = the quantity x squared minus 36 over the quantity 4x minus 24

To find : What are the discontinuities of the function .

Solution : We have given

f(x) = $\frac{x^{2}- 36 }{4x - 24}$.

On factoring $x^{2}- 36 = (x+6) (x -6)$

4x - 24 = 4 ( x -6 ).

Then , f(x) = $\frac{(x-6) (x +6) }{4(x -6)}$.

f(x) =  $\frac{(x-6)(x +6) }{4(x -6)}$.

A point of discontinuity occurs when a number is both a zero of the numerator and denominator.

Hence , at x = 6 both numerator and denominator is zero.

Therefore, Discontinuities of the function is x = 6  .