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Find the domain of f(s)--4, Express the domain in internal netation, SHOW WORK OR NO CREDIT 3.

Find the domain of f(s)--4, Express the domain in internal netation, SHOW WORK OR NO CREDIT 3.

Algebra and Trigonometry (6th Edition)
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
**Educational Content: Domain and Simplification of Functions** **3. Problem Statement** Find the domain of \( f(x) = \sqrt{x - 4} \). Express the domain in interval notation. *Instruction*: Show your work. No credit will be given for simply stating the answer without justification. --- **4. Problem Set** **Given Functions:** \( f(x) = 2x^2 + 5x \) and \( g(x) = x - 3 \). *Objective:* Find and simplify the following expressions. - **a.** \( (f - g)(x) \) - **b.** Domain of \( (f - g)(x) \) in interval notation - **c.** \( \left(\frac{f}{g}\right)(x) \) - **d.** Domain of \( \left(\frac{f}{g}\right)(x) \) in interval notation --- **5. Additional Problem Set** **Given Functions:** \( f(x) = x + 7 \) and \( g(x) = 4x^2 - 2 \). *Objective:* Find and simplify the following expressions. - **a.** \( (f \circ g)(x) \) - **b.** \( (g \circ f)(x) \) --- For each task, ensure to illustrate clarity in expressing domains and steps involved in simplification. Provide detailed solutions and justifications to enhance understanding.
Transcribed Image Text:**Educational Content: Domain and Simplification of Functions** **3. Problem Statement** Find the domain of \( f(x) = \sqrt{x - 4} \). Express the domain in interval notation. *Instruction*: Show your work. No credit will be given for simply stating the answer without justification. --- **4. Problem Set** **Given Functions:** \( f(x) = 2x^2 + 5x \) and \( g(x) = x - 3 \). *Objective:* Find and simplify the following expressions. - **a.** \( (f - g)(x) \) - **b.** Domain of \( (f - g)(x) \) in interval notation - **c.** \( \left(\frac{f}{g}\right)(x) \) - **d.** Domain of \( \left(\frac{f}{g}\right)(x) \) in interval notation --- **5. Additional Problem Set** **Given Functions:** \( f(x) = x + 7 \) and \( g(x) = 4x^2 - 2 \). *Objective:* Find and simplify the following expressions. - **a.** \( (f \circ g)(x) \) - **b.** \( (g \circ f)(x) \) --- For each task, ensure to illustrate clarity in expressing domains and steps involved in simplification. Provide detailed solutions and justifications to enhance understanding.
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