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

Find all critical numbers of:

g(x)= sqrt(x^{2}-4)

and

f(x)= (1)/(x^{2}-9)

2. Relevant equations

n/a

3. The attempt at a solution

1) sqrt(x^{2}-4)

simplified to x(x-2)(x+2)^{-1/2}(please check)

and got zeroes as x=0, x=2, x=-2

and I got confused because if you do g(2) and g(-2) it equals zero. For some reason I can't tell if they are defined or undefined. x=0 works, so that is a critical number. The other two are throwing me off.

2) (1)/(x^{2}-9)

zeroes were x=-3, x=3, x=0. Plugging 3 and -3 back into f(x) gave me undefined, so I'm pretty sure 0 is the only critical number.

If you could please check the second and help with the first that would be great. Thank you

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# Homework Help: Finding critical numbers

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