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Find the inverse of the following: а. f(x) %3D 10х? — 9 7x+18 b. g(x) = 2

Find the inverse of the following: а. f(x) %3D 10х? — 9 7x+18 b. g(x) = 2

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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**Find the Inverse of the Following Functions** Consider the given functions: a. \( f(x) = 10x^2 - 9 \) b. \( g(x) = \frac{7x + 18}{2} \) Your task is to determine the inverse of each function. Remember, to find the inverse of a function, interchange \( x \) and \( y \) and solve for \( y \). Here is a brief outline on how to approach this for each function: 1. **For the function \( f(x) = 10x^2 - 9 \):** - Replace \( f(x) \) with \( y \): \( y = 10x^2 - 9 \) - Swap \( x \) and \( y \): \( x = 10y^2 - 9 \) - Solve for \( y \) to find \( f^{-1}(x) \). 2. **For the function \( g(x) = \frac{7x + 18}{2} \):** - Replace \( g(x) \) with \( y \): \( y = \frac{7x + 18}{2} \) - Swap \( x \) and \( y \): \( x = \frac{7y + 18}{2} \) - Solve for \( y \) to find \( g^{-1}(x) \). Follow these steps to derive the inverses of the given functions. When performing these steps, ensure your algebraic manipulations are accurate to obtain the correct inverses.
Transcribed Image Text:**Find the Inverse of the Following Functions** Consider the given functions: a. \( f(x) = 10x^2 - 9 \) b. \( g(x) = \frac{7x + 18}{2} \) Your task is to determine the inverse of each function. Remember, to find the inverse of a function, interchange \( x \) and \( y \) and solve for \( y \). Here is a brief outline on how to approach this for each function: 1. **For the function \( f(x) = 10x^2 - 9 \):** - Replace \( f(x) \) with \( y \): \( y = 10x^2 - 9 \) - Swap \( x \) and \( y \): \( x = 10y^2 - 9 \) - Solve for \( y \) to find \( f^{-1}(x) \). 2. **For the function \( g(x) = \frac{7x + 18}{2} \):** - Replace \( g(x) \) with \( y \): \( y = \frac{7x + 18}{2} \) - Swap \( x \) and \( y \): \( x = \frac{7y + 18}{2} \) - Solve for \( y \) to find \( g^{-1}(x) \). Follow these steps to derive the inverses of the given functions. When performing these steps, ensure your algebraic manipulations are accurate to obtain the correct inverses.
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