Linear functions, inverses, and derivatives Consider the general linear function y = f1x2 = mx + b, where m # 0 and b are constants. a. Write the inverse of f in the form y = f-11x2. d b. Find the derivative of the inverse 1f -11x22. dx c. Consider the specific case f1x2 = 2x 6. Graph f and f-1, and find the slope of each line.

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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Linear functions, inverses, and derivatives Consider the general linear
function y = f1x2 = mx + b, where m # 0 and b are constants.
a. Write the inverse of f in the form y = f-11x2.
d
b. Find the derivative of the inverse
1f -11x22.
dx
c. Consider the specific case f1x2
= 2x
6. Graph f and f-1, and find the slope of
each line.
Transcribed Image Text:Linear functions, inverses, and derivatives Consider the general linear function y = f1x2 = mx + b, where m # 0 and b are constants. a. Write the inverse of f in the form y = f-11x2. d b. Find the derivative of the inverse 1f -11x22. dx c. Consider the specific case f1x2 = 2x 6. Graph f and f-1, and find the slope of each line.
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