Show that the function f(x) = ax + b from R to R is invertible. where a and b are constants, with a ? 0. and find the inverse of f.
SolutionStep 1In the problem we have to prove function f(x) = ax + b from R to R invertible and Also find inverse.Let us assume that the function is defined that f(x) = ax + b = yWe have to Consider that f(x) is one to one function then Then, y = ax + bSubtracting b on both the sides we get, y - b = ax + b - b y - b = axNow Divide by a on both the sides we get, = xSo, for inverse switch x and y = yThis leads to a function p such that R to R can be p(x) =
Textbook: Discrete Mathematics and Its Applications
Author: Kenneth Rosen
This full solution covers the following key subjects: constants, Find, function, Inverse, invertible. This expansive textbook survival guide covers 101 chapters, and 4221 solutions. The answer to “Show that the function f(x) = ax + b from R to R is invertible. where a and b are constants, with a ? 0. and find the inverse of f.” is broken down into a number of easy to follow steps, and 31 words. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. Since the solution to 39E from 2.3 chapter was answered, more than 378 students have viewed the full step-by-step answer. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. The full step-by-step solution to problem: 39E from chapter: 2.3 was answered by , our top Math solution expert on 06/21/17, 07:45AM.