Answer to Question #320011 in Calculus for shi

Question

Determine wether the following functions is continuous on the given interval. f(x) = √4-x²

Answer 1

$f\,\,is\,\,defined\,\,for\,\,x\in \left[ -2,2 \right] \\f\,\,is\,\,continuous\,\,on\,\,\left[ -2,2 \right] , \sin ce\,\,it\,\,is\,\,a\,\,composition\,\,of\\h\left( x \right) =4-x^2-continuous\,\,on\,\,\mathbb{R} \,\,as\,\,a\,\,polynomial\\g\left( x \right) =\sqrt{x}-continuous\,\,on\,\,\left[ 0,+\infty \left. \right) \right.$