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# Quadratic Equations and Functions: Sum, Difference, and Product of Two Functions Suppose that the functions \( f \) and \( g \) are defined for all real numbers \( x \) as follows: \[ f(x) = x^3 \] \[ g(x) = 5x^2 \] Write the expressions for \( (f+g)(x) \) and \( (f \cdot g)(x) \) and evaluate \( (f-g)(-1) \). ### Tasks 1. Calculate \( (f+g)(x) \). 2. Calculate \( (f \cdot g)(x) \). 3. Evaluate \( (f-g)(-1) \). ### Input Fields - \( (f+g)(x) = \) [________] - \( (f \cdot g)(x) = \) [________] - \( (f-g)(-1) = \) [________] ### Interactivity - **Explanation**: Button to reveal detailed solutions and explanations for each calculation. - **Check**: Button to verify your answers. This exercise helps reinforce understanding of function operations, including their sum, product, and evaluation at specific points.

# Quadratic Equations and Functions: Sum, Difference, and Product of Two Functions Suppose that the functions \( f \) and \( g \) are defined for all real numbers \( x \) as follows: \[ f(x) = x^3 \] \[ g(x) = 5x^2 \] Write the expressions for \( (f+g)(x) \) and \( (f \cdot g)(x) \) and evaluate \( (f-g)(-1) \). ### Tasks 1. Calculate \( (f+g)(x) \). 2. Calculate \( (f \cdot g)(x) \). 3. Evaluate \( (f-g)(-1) \). ### Input Fields - \( (f+g)(x) = \) [________] - \( (f \cdot g)(x) = \) [________] - \( (f-g)(-1) = \) [________] ### Interactivity - **Explanation**: Button to reveal detailed solutions and explanations for each calculation. - **Check**: Button to verify your answers. This exercise helps reinforce understanding of function operations, including their sum, product, and evaluation at specific points.

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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# Quadratic Equations and Functions: Sum, Difference, and Product of Two Functions Suppose that the functions \( f \) and \( g \) are defined for all real numbers \( x \) as follows: \[ f(x) = x^3 \] \[ g(x) = 5x^2 \] Write the expressions for \( (f+g)(x) \) and \( (f \cdot g)(x) \) and evaluate \( (f-g)(-1) \). ### Tasks 1. Calculate \( (f+g)(x) \). 2. Calculate \( (f \cdot g)(x) \). 3. Evaluate \( (f-g)(-1) \). ### Input Fields - \( (f+g)(x) = \) [________] - \( (f \cdot g)(x) = \) [________] - \( (f-g)(-1) = \) [________] ### Interactivity - **Explanation**: Button to reveal detailed solutions and explanations for each calculation. - **Check**: Button to verify your answers. This exercise helps reinforce understanding of function operations, including their sum, product, and evaluation at specific points.
Transcribed Image Text:# Quadratic Equations and Functions: Sum, Difference, and Product of Two Functions Suppose that the functions \( f \) and \( g \) are defined for all real numbers \( x \) as follows: \[ f(x) = x^3 \] \[ g(x) = 5x^2 \] Write the expressions for \( (f+g)(x) \) and \( (f \cdot g)(x) \) and evaluate \( (f-g)(-1) \). ### Tasks 1. Calculate \( (f+g)(x) \). 2. Calculate \( (f \cdot g)(x) \). 3. Evaluate \( (f-g)(-1) \). ### Input Fields - \( (f+g)(x) = \) [________] - \( (f \cdot g)(x) = \) [________] - \( (f-g)(-1) = \) [________] ### Interactivity - **Explanation**: Button to reveal detailed solutions and explanations for each calculation. - **Check**: Button to verify your answers. This exercise helps reinforce understanding of function operations, including their sum, product, and evaluation at specific points.
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Given:  f(x)=x3, g(x)=5x2

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