For f(x) = 1/(x^2−4) and g(x) = √ (x − 1), determine the subset of the domain of g on which the composition f ◦ g is well-defined, and then determine the subset of the domain of f on which the composition g ◦ f is well-defined. In other words, determine the domains of f ◦ g and g ◦ f. Then, find formulas for (f ◦ g)(x) and (g ◦ f)(x). • If you use a definition, explicitly cite it by using the phrase “by the definition of . . . .” • If you use a theorem (or a rule, a test), explicitly cite it by using the phrases “by theorem . . . .” • Explain the quantity each symbol represent in word problems. Use phrases like “let x be the height of a rectangle” or “let t represent time in seconds.”
For f(x) = 1/(x^2−4) and g(x) = √ (x − 1), determine the subset of the domain of g on which the composition f ◦ g is well-defined, and then determine the subset of the domain of f on which the composition g ◦ f is well-defined. In other words, determine the domains of f ◦ g and g ◦ f. Then, find formulas for (f ◦ g)(x) and (g ◦ f)(x). • If you use a definition, explicitly cite it by using the phrase “by the definition of . . . .” • If you use a theorem (or a rule, a test), explicitly cite it by using the phrases “by theorem . . . .” • Explain the quantity each symbol represent in word problems. Use phrases like “let x be the height of a rectangle” or “let t represent time in seconds.”
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 54E
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For f(x) = 1/(x^2−4) and g(x) = √ (x − 1), determine the subset of the domain of g on which the composition f ◦ g is well-defined, and then determine the subset of the domain of f on which the composition g ◦ f is well-defined. In other words, determine the domains of f ◦ g and g ◦ f. Then, find formulas for (f ◦ g)(x) and (g ◦ f)(x).
• If you use a definition, explicitly cite it by using the phrase “by the definition of . . . .” • If you use a theorem (or a rule, a test), explicitly cite it by using the phrases “by theorem . . . .” • Explain the quantity each symbol represent in word problems. Use phrases like “let x be the height of a rectangle” or “let t represent time in seconds.”
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