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form of y=f(x (x,५) y = 4 2 (x₁9) x = 4

form of y=f(x (x,५) y = 4 2 (x₁9) x = 4

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Form of y=f(X)

**Topic: Function Notation in Mathematics** In mathematics, the notation \( y = f(x) \) is used to denote a function. Specifically, \( f \) is the function, \( x \) is the variable or input, and \( y \) is the output or the value of the function at \( x \). ### Explanation: 1. **Function Form:** The function is denoted as \( y = f(x) \). This indicates that \( y \) is a function of \( x \). 2. **Specific Values:** When given specific values: - If \( x = a \), then \( y = f(a) \). - For example, if \( f(x) = 4 \) when \( x = 2 \), then plugging in \( x = 2 \) into the function \( f \) results in \( f(2) = 4 \). ### Example: Consider the function where \( y = f(x) \) and we have: - \( f(2) = 4 \) - Therefore, when \( x = 2 \), the output \( y \) is 4. Understanding this function notation is fundamental in various fields of study, including algebra, calculus, and other areas of mathematics. This notation allows us to precisely define the relationship between variables and to perform various operations and transformations on functions.
Transcribed Image Text:**Topic: Function Notation in Mathematics** In mathematics, the notation \( y = f(x) \) is used to denote a function. Specifically, \( f \) is the function, \( x \) is the variable or input, and \( y \) is the output or the value of the function at \( x \). ### Explanation: 1. **Function Form:** The function is denoted as \( y = f(x) \). This indicates that \( y \) is a function of \( x \). 2. **Specific Values:** When given specific values: - If \( x = a \), then \( y = f(a) \). - For example, if \( f(x) = 4 \) when \( x = 2 \), then plugging in \( x = 2 \) into the function \( f \) results in \( f(2) = 4 \). ### Example: Consider the function where \( y = f(x) \) and we have: - \( f(2) = 4 \) - Therefore, when \( x = 2 \), the output \( y \) is 4. Understanding this function notation is fundamental in various fields of study, including algebra, calculus, and other areas of mathematics. This notation allows us to precisely define the relationship between variables and to perform various operations and transformations on functions.
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