(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

This is a piece wise function of course. f(x) =

(x^{2}-4) / (x-2) if x is less than two.

ax^{2}- bx + 1 if x is greater than or equal to 2, or less than three.

4x - a + b if x is greater than or equal to three.

2. Relevant equations

3. The attempt at a solution

Alright, I know enough to factor the top of the fist equation and get x+2. That means when x is two, f(x) is four. We can use f(x) in this case because we are making the function continuous. I've gotten as far as plugging in this value in the second equation and getting

4 = a4 - b2 + 1

but I don't know what to do from here, or how to get the values of a and b. I think I subtract one from the right and get

3 = a4 - 2b

Now I am definitely stuck.

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# Find the values of a and b that make f continuous everywhere

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