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8. Let f(x) = x² - 3x + 1 and g(x) 2x² + 5x - 3. a. Find f(x) - g(x + 2). Simplify as much as possible. = (-00) -$)U(-¾. £) b. Find g (b²) + g(b). Simplify as much as possible. c. Find the difference quotient for f(x). Simplify as much as possible. a. f(x) < (x+2) =x²-3x+1-(2(x+2) ²¹+5(x+2)-3) =x²-3x+1-(26x² + 4x+ 4)+ 5x+10-3)

8. Let f(x) = x² - 3x + 1 and g(x) 2x² + 5x - 3. a. Find f(x) - g(x + 2). Simplify as much as possible. = (-00) -$)U(-¾. £) b. Find g (b²) + g(b). Simplify as much as possible. c. Find the difference quotient for f(x). Simplify as much as possible. a. f(x) < (x+2) =x²-3x+1-(2(x+2) ²¹+5(x+2)-3) =x²-3x+1-(26x² + 4x+ 4)+ 5x+10-3)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem 8** Given: - \( f(x) = x^2 - 3x + 1 \) - \( g(x) = 2x^2 + 5x - 3 \) ### Tasks: a. **Find \( f(x) - g(x + 2) \). Simplify as much as possible.** b. **Find \( g(b) + g(b) \). Simplify as much as possible.** c. **Find the difference quotient for \( f(x) \). Simplify as much as possible.** ### Notes: - **a.** In this task, you will substitute \( x + 2 \) into the function \( g(x) \) and then subtract the result from \( f(x) \). - **b.** You are asked to calculate the value of \( g(b) \) and then add it to itself. - **c.** The difference quotient is a fundamental concept in calculus, often expressed as \( \frac{f(x+h) - f(x)}{h} \). Simplify the expression using algebraic manipulations. ### Diagram: The image contains a visual representation of the function operations but does not provide any explicit graphs or detailed diagrams related to the tasks. It shows notations for the functions and potentially some interim calculations. Ensure to follow these steps systematically to achieve the correct solutions for each part.
Transcribed Image Text:**Problem 8** Given: - \( f(x) = x^2 - 3x + 1 \) - \( g(x) = 2x^2 + 5x - 3 \) ### Tasks: a. **Find \( f(x) - g(x + 2) \). Simplify as much as possible.** b. **Find \( g(b) + g(b) \). Simplify as much as possible.** c. **Find the difference quotient for \( f(x) \). Simplify as much as possible.** ### Notes: - **a.** In this task, you will substitute \( x + 2 \) into the function \( g(x) \) and then subtract the result from \( f(x) \). - **b.** You are asked to calculate the value of \( g(b) \) and then add it to itself. - **c.** The difference quotient is a fundamental concept in calculus, often expressed as \( \frac{f(x+h) - f(x)}{h} \). Simplify the expression using algebraic manipulations. ### Diagram: The image contains a visual representation of the function operations but does not provide any explicit graphs or detailed diagrams related to the tasks. It shows notations for the functions and potentially some interim calculations. Ensure to follow these steps systematically to achieve the correct solutions for each part.
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