Answer to Question #125402 in Algebra for EMMANUEL

Question

Find the domains of f(x)= (4-x²)^1/2 and h(x)= (3-x)^1/2.

Answer 1

Given $f(x)=\sqrt{4-x^2}$ ,$h(x)=\sqrt{3-x},$

$f(x)$ is defined if $4-x^2\geq 0\implies(2-x)(2+x)\geq0$ . Thus, $x\in[-2,2]$ ,hence the domain of $f$ is $D_f=[-2,2]$ .

Now, $h(x)$ is defined if $3-x\geq0\implies x\in(-\infty,3]$ ,hence the domain of $h$ is $D_h=(-\infty,3]$ .