Question # Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval. g(x)=2\sqrt{3}-x,(-\infty

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ANSWERED Use the definition of continuity and the properties of limits to show that the function is continuous on the given interval.
$$\displaystyle{g{{\left({x}\right)}}}={2}\sqrt{{{3}}}-{x},{\left(-\infty,{3}\right]}$$ 2021-06-21
Polynomial and root functions are continuous over their domains.
Polynomials such as 3— x are continous for all real numbers, so it is contintious and also $$\displaystyle\geq{0}$$ for the given interval.
The domains of root functions are the values for which the radicand (value inside the radical) is $$\displaystyle\geq{0}$$.
The composition of 3 — 2 and the root function will also be continuous ("theorem 9”) since both are continuous on their own.
$$\displaystyle\sqrt{{{3}-{x}}}$$
The ”2” can be considered a constant function which is also continuous. The product of two continuous functions is also continuous. So g(z) is eontintntis far the-siven interral.