Find the value of p and q that make the function continuous

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Homework Statement



Find the value of p and q that make the function continuous

Homework Equations


f(x)= x-2 if x≥2
\sqrt{p-x^{2}} -2<x<2
q-x if x≤-2

The Attempt at a Solution


lim f(x)= x-2
n→2+

lim f(x)=q-x
n→-2

I really have no idea how to continue,the teacher never explained this and I have a test tomorrow please help!
 
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Does q= -2 and p=4 ?
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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