what is the domain of the function f give by f(x) = root(x^2-4)/x-3. is it x:IxI>2nd x not equals 3 or just x:x equal or lager than 2 and x is not eqals 3?

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The first choice with the abs x>2 and x not equal to 3 works.  Even a negative number less than -2 when squared will give a positive number larger than 4 and thus a real number square root instead of an imaginary number.  x cannot be 3 or the denominator would be 0.