Continuity: Find points where y = (x + 1)/(x^2 - 4x + 3) is

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chickyme89

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Find the points, if any, at which the function is not continuous.

19. y = (x + 1)/(x^2 - 4x + 3)

I attempted to factor out the denominator. My result was (x-3)(x-1). The answer however is 1. But I don't understand why it was not 3 as well.

37. What value should be assigned to 'a' to make the following function continuous at x = 3?

. . . . . ./ x^3 for x < 3
f(x)= <
. . . . . .\ 2ax for x > 3

I can't seem to figure out how to do this problem. I started by graphing it, and tracing the value where x=3, but of course it was non-existant. I do know that the answer is 4/3, but how does one reach this conclusion?
 
A rational expression is continuous everywhere except where the denominator is 0. 3 ought to be a solution also.


For the second one, I got a=9/2. Are you sure the answer is 4/3?.
Maybe I am erring, though.
 
I had posted the same things as galactus but deleted my post when I saw that the correct answer is 4/3.

If your book failed to mention 3 as a discontinuity in 19, then I'm willing to bet it also made a mistake with 37. a=9/2 is the point that makes your piecewise continuous, as (3,27) should be the 'connection' when f(x)=3.

think of it this way, for your function to be continuous, every point must have a limit. When x approaches 3 from the left, it's limit is 27. When x approaches 3 from the right, is 6a. For it to be continuous, 27 must equal 6a. Thus, a = 9/2.
 
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