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Exercises Functions

Example 4 from Algebra and Trigonometry, 3.2 Domain and Range

Finding the Domain of a Function with an Even Root

Find the domain of the function $f (x) = \sqrt{7 - x} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
When there is an even root in the formula, we exclude any real numbers that result in a negative number in the radicand.

Set the radicand greater than or equal to zero and solve for $x .$

$\begin{matrix} 7 - x & \geq & 0 \\ - x & \geq & −7 \\ x & \leq & 7 \end{matrix}$

Now, we will exclude any number greater than 7 from the domain. The answers are all real numbers less than or equal to $7,$ or $(- \infty, 7] .$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Find the domain of the function $f (x) = \sqrt{5 + 2 x} .$

How did it go?

PreviousFinding the Domain of a Function Involving a Denominator Next Describing Sets on the Real-Number Line

From Algebra and Trigonometry (1st edition) by OpenStax (Rice University), section 3.2, licensed under CC BY 4.0. Original at openstax.org. We split the solution into steps; the words, numbers and figures are the book's. OpenStax doesn't endorse this site.