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Finding the Domain of a Function Involving a Denominator · Physics Playground

Exercises Functions

Example 3 from Algebra and Trigonometry, 3.2 Domain and Range

Finding the Domain of a Function Involving a Denominator

Find the domain of the function $f (x) = \frac{x + 1}{2 - x} .$

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 a denominator, we want to include only values of the input that do not force the denominator to be zero. So, we will set the denominator equal to 0 and solve for $x .$

$\begin{matrix} 2 - x & = & 0 \\ - x & = & −2 \\ x & = & 2 \end{matrix}$
Now, we will exclude 2 from the domain. The answers are all real numbers where $x < 2$ or $x > 2$ as shown in Figure 4. We can use a symbol known as the union, $\cup,$ to combine the two sets. In interval notation, we write the solution: $(−∞, 2) \cup (2, \infty) .$

Figure 4

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: $f (x) = \frac{1 + 4 x}{2 x - 1} .$

How did it go?

PreviousFinding the Domain of a Function Next Finding the Domain of a Function with an Even Root

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.