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

Matrices
ANSWERED
asked 2021-06-20

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

Answers (1)

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.
0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours
...