Determine wether the following functions is continuous on the given interval. f(x) = √4-x²
f is defined for x∈[−2,2]f is continuous on [−2,2],since it is a composition ofh(x)=4−x2−continuous on R as a polynomialg(x)=x−continuous on [0,+∞)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.fisdefinedforx∈[−2,2]fiscontinuouson[−2,2],sinceitisacompositionofh(x)=4−x2−continuousonRasapolynomialg(x)=x−continuouson[0,+∞)
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