**Composite Functions and Domain Analysis** For the functions \( f(x) = \frac{2}{x-9} \) and \( g(x) = \frac{1}{x} \), evaluate the following composite functions and determine the domain of each: 1. (a) \( f \circ g \) 2. (b) \( g \circ f \) 3. (c) \( f \circ f \) 4. (d) \( g \circ g \) **Task:** (a) Calculate \( (f \circ g)(x) = \) ________ (Simplify your answer.)
**Composite Functions and Domain Analysis** For the functions \( f(x) = \frac{2}{x-9} \) and \( g(x) = \frac{1}{x} \), evaluate the following composite functions and determine the domain of each: 1. (a) \( f \circ g \) 2. (b) \( g \circ f \) 3. (c) \( f \circ f \) 4. (d) \( g \circ g \) **Task:** (a) Calculate \( (f \circ g)(x) = \) ________ (Simplify your answer.)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question

Transcribed Image Text:**Composite Functions and Domain Analysis**
For the functions \( f(x) = \frac{2}{x-9} \) and \( g(x) = \frac{1}{x} \), evaluate the following composite functions and determine the domain of each:
1. (a) \( f \circ g \)
2. (b) \( g \circ f \)
3. (c) \( f \circ f \)
4. (d) \( g \circ g \)
**Task:**
(a) Calculate \( (f \circ g)(x) = \) ________ (Simplify your answer.)
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