Question

Determine whether the following functions are continuous on the given interval. Show your complete solution.

1. ƒ(𝑥)=√4−𝑥2 ;[−2,2]

2. ƒ(𝑥)=3𝑥2 −𝑥+5 ; (−∞,+∞)

Answer 1

$f\left( x \right) =\sqrt{4-x^2}$ is continuous on $D\left( f \right) =\left[ -2,2 \right]$ , since it is a composition of polynomial function $4-x^2$ and power function $\sqrt{x}$

$f\left( x \right) =3x^2-x+5$ is continuous on $\left( -\infty ,+\infty \right)$ since it is polynomial function.