Continuity and continuous functions

• Oct 3rd 2012, 01:53 PM
phenol
Continuity and continuous functions
Hi,
Would anyone be able to tell me how I'd go about obtaining this answer? Here's what I've done so far.

-2(x) + b => -2(2) + b => -4 + b (from the left side)

-24/x-b => -24/(2)-b (from the right side)

the part/step I don't understand is when you add them together and come out with . . .

(-4+b)(2-b) = -24 ??? How do you come up with this?

I know the next step is multiply out and move -24 to the left so that you set it to = 0.

-8+4b+2b-b2 =-24
-(b2-6b+8)=-24
b2-6b+8=24
b2-6b-16 = 0
(b-8)(b+2) = 0

So the answer to this problem is b=8 (because it has a greater absolute value than 2)

Hope this isn't confusing to anyone reading this. Any help would be greatly appreciated! Thanks, Ana

Here's the problem
There are exactly two values for b which make f (x) a continuous function at x = 2. The one with the greater absolute value is b=?

Attachment 25029
• Oct 3rd 2012, 02:26 PM
Plato
Re: Continuity and continuous functions
Quote:

Originally Posted by phenol
Here's the problem
There are exactly two values for b which make f (x) a continuous function at x = 2. The one with the greater absolute value is b=?
Attachment 25029

If that is the correct problem then $\displaystyle b=8\text{ or }b=-2.$
• Oct 3rd 2012, 02:54 PM
HallsofIvy
Re: Continuity and continuous functions
Quote:

Originally Posted by phenol
Hi,
Would anyone be able to tell me how I'd go about obtaining this answer? Here's what I've done so far.

-2(x) + b => -2(2) + b => -4 + b (from the left side)

-24/x-b => -24/(2)-b (from the right side)

the part/step I don't understand is when you add them together and come out with . . .

You don't "add them together"- especially when talking about mathematics don't use the term "add" to mean just combing two things!
What you mean is "in order to be continuous those two one sided limits must be the same so -4+ b= -24/(2- b).

Quote:

(-4+b)(2-b) = -24 ??? How do you come up with this?
Multiply by both sides by 2- b.

Quote:

I know the next step is multiply out and move -24 to the left so that you set it to = 0.

-8+4b+2b-b2 =-24
-(b2-6b+8)=-24
b2-6b+8=24
b2-6b-16 = 0
(b-8)(b+2) = 0

So the answer to this problem is b=8 (because it has a greater absolute value than 2)

Hope this isn't confusing to anyone reading this. Any help would be greatly appreciated! Thanks, Ana

Here's the problem
There are exactly two values for b which make f (x) a continuous function at x = 2. The one with the greater absolute value is b=?

Attachment 25029