Chapter 1.4, Problem 83E

To determine

To find the domain of the given function $f(x)=\sqrt{100-x^2}$

Answer to Problem 83E

Domain: $[-10,10]$

Explanation of Solution

Given:

Function: $f(x)=\sqrt{100-x^2}$

Calculation:

Domain of a function is the set of all real numbers for which the function is defined.

To find the domain of the given function $f(x)=\sqrt{100-x^2}$

Check for all the values of $x$ that makes the numerator and denominator of the function zero.

Here, In the given function, when substituting the value of $x=\pm 10$ , the function becomes zero. So the value of $x$ in the numerator should be greater than 10.

Also, the function is defined only when

  $\begin{array}{c}100-x^2\ge 0\\ x^2\le 100\\ \left|x\right|\le 10\\ x\in [-10,10]\end{array}$

So, the domain of the function is the set of all the real numbers in the interval $[-10,10]$ .

Conclusion:

Therefore, the domain of the function $f(x)=\sqrt{100-x^2}$ is $[-10,10]$