Respuesta :
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:
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) = [tex]\frac{x^{2}- 36 }{4x - 24}[/tex].
On factoring [tex]x^{2}- 36 = (x+6) (x -6)[/tex]
4x - 24 = 4 ( x -6 ).
Then , f(x) = [tex]\frac{(x-6) (x +6) }{4(x -6)}[/tex].
f(x) = [tex]\frac{(x-6)(x +6) }{4(x -6)}[/tex].
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 .
