# Chapter 2 - Nonlinear Functions - 2.1 Properties of Functions - 2.1 Exercises - Page 54: 21

$$f(x)=\sqrt {4-x^{2}}$$ the values $x$ for $f(x)$ is defined when: $$4-x^{2}\geq 0$$ we can find all zeros $f(x)$ $$4-x^{2} = (2-x)(2+x) = 0$$ $\Rightarrow$ $$x=\pm 2,$$ this numbers form the intervals $(-\infty,-2), (-2,2)$ and $(2,\infty)$. we observe that the values in the interval $[-2,2]$ which satisfy the inequality So domain of the function $f (x)$ is $[-2,2]$ .

#### Work Step by Step

$$f(x)=\sqrt {4-x^{2}}$$ the values $x$ for $f(x)$ is defined when: $$4-x^{2}\geq 0$$ we can find all zeros $f(x)$ $$4-x^{2} = (2-x)(2+x) = 0$$ $\Rightarrow$ $$x=\pm 2,$$ this numbers form the intervals $(-\infty,-2), (-2,2)$ and $(2,\infty)$. we observe that the values in the interval $[-2,2]$ which satisfy the inequality So domain of the function $f (x)$ is $[-2,2]$ .

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.