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Which statement describes whether the function is continuous at x = 2?
O The function is continuous at x = 2 because f(2) exists.
O The function is continuous at x = 2 because lim f(x) exists.
X-2
The function is not continuous at x = 2 because f(2) does not exist.
The function is not continuous at x = 2 because lim f(x) does not equal f(2).
X-2

Which statement describes whether the function is continuous at x 2 O The function is continuous at x 2 because f2 exists O The function is continuous at x 2 be class=

Respuesta :

Answer: (b)

Step-by-step explanation:

Given

The function is given as

[tex]f(x)=\dfrac{x^2-12x+20}{x-2}[/tex]

Solving the function

[tex]f(x)=\dfrac{x^2-2x-10x+20}{x-2}\\\\f(x)=\dfrac{(x-2)(x-10)}{(x-2)}\\\\f(x)=x-10[/tex]

for [tex]x=2[/tex]

[tex]f(2)=2-10\\f(2)=-8[/tex]

The function is continuous at [tex]x=2[/tex] because [tex]\lim_{x \to 2} f(x)[/tex] exists.

If the limit exists at a point, then the function is continuous.  

Answer:

on edge its fs not b or c

Step-by-step explanation:

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