Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device (should be able to scroll to see them) and some of the menu items will be cut off due to the narrow screen width.
Section 1.1 : Review : Functions
26. Find the domain of \(g\left( x \right) = \sqrt {25 - {x^2}} \).
Show SolutionIn this case we need to avoid square roots of negative numbers so we need to require,
\[25 - {x^2} \ge 0\]Note that once we have the original inequality written down we can do a little rewriting of things as follows to make things a little easier to see.
\[{x^2} \le 25\hspace{0.25in}\hspace{0.25in} \Rightarrow \hspace{0.25in}\,\,\,\,\, - 5 \le x \le 5\]At this point it should be pretty easy to find the values of \(x\) that will keep the quantity under the radical positive or zero so we won’t need to do a number line or sign table to determine the range.
The domain is then,
\[{\mbox{Domain : }} - 5 \le x \le 5\]