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CONCEPT PREVIEW Perform the operations mentally, and write the answers without doing intermediate steps. (√28 - √14) (√28 + √14)
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Ch. R - Algebra Review
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891
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TOC.tableOfContents
- Ch. R - Algebra Review381
- Ch. 1 - Trigonometric Functions188
- Ch. 2 - Acute Angles and Right Triangles168
- Ch. 3 - Radian Measure and The Unit Circle155
- Ch. 4 - Graphs of the Circular Functions100
- Ch. 5 - Trigonometric Identities238
- Ch. 6 - Inverse Circular Functions and Trigonometric Equations158
- Ch. 7 - Applications of Trigonometry and Vectors148
- Ch. 8 - Complex Numbers, Polar Equations, and Parametric Equations15
Lial12th EditionTrigonometryISBN: 9780136552161, 9780135440780, 9780136881117, 9780135440827, 9780135924891Non è quello che usi tu?Cambia libro di testo
Capitolo 1, Problema 11
Find the domain of each rational expression. See Example 1. (x + 3) / (x - 6)
Guida verificata passo dopo passo1
Identify the rational expression given, which is \(\frac{x + 3}{x - 6}\).
Recall that the domain of a rational expression includes all real numbers except those that make the denominator zero, because division by zero is undefined.
Set the denominator equal to zero to find the values to exclude: \(x - 6 = 0\).
Solve the equation \(x - 6 = 0\) to find \(x = 6\).
Conclude that the domain is all real numbers except \(x = 6\), which can be written in interval notation as \((-\infty, 6) \cup (6, \infty)\).
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Domain of a Function
The domain of a function is the set of all input values (x-values) for which the function is defined. For rational expressions, the domain excludes values that make the denominator zero, as division by zero is undefined.
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Percorso guidato
3:43
Finding the Domain of an Equation
Rational Expressions
A rational expression is a fraction where both the numerator and denominator are polynomials. Understanding how to simplify and analyze these expressions is essential, especially identifying values that cause the denominator to be zero.
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Percorso guidato
2:58Rationalizing Denominators
Finding Restrictions on the Domain
To find the domain of a rational expression, set the denominator equal to zero and solve for x. The solutions are excluded from the domain because they make the expression undefined. The domain is all real numbers except these excluded values.
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Percorso guidato
3:43Finding the Domain of an Equation
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