SOLUTION: Not sure if this is the right section or not. Anyway, I'm struggling with Piecewise-defined functions. My question is about finding all the values of b that make the function con

Algebra ->  Functions -> SOLUTION: Not sure if this is the right section or not. Anyway, I'm struggling with Piecewise-defined functions. My question is about finding all the values of b that make the function con      Log On


   

Question 1067237: Not sure if this is the right section or not.
Anyway, I'm struggling with Piecewise-defined functions. My question is about finding all the values of b that make the function continuous everywhere.
f(x)= (x^2-4)/x-2 x < 2,
[b-cos(pix/2)]^2. x >= 2
Not sure how to solve it help would be great. I think I'm supposed to evaluate each at the limit as x approaches 2 but am not sure.
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
The only point you're concerned with is x=2 because the limit from the left must equal the limit from the right.
So set the two functions equal to each other when x=2 and solve for b to make it so.
So,
%28x%5E2-4%29%2F%28x-2%29=x%2B2 except when x=2
So then,
x%2B2=b-cos%28%28pi%2F2%29x%29%29
So now take the limit as x approaches 2,
2%2B2=b-cos%28%28pi%2F2%292%29
4=b-cos%28pi%29
4=b-%28-1%29
4=b%2B1
b=3
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