iv. Show that f is NOT one-to-one. (Give a counterexample.) v. Find an interval I where f is one-to-one. Moreover, find the inverse of f defined on I. vi. Verify that f and f are inverses of each other. (Hint: Use the composition of functions.)

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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please answer iv to vi. 

1. Consider the equation y = f(x) = V1+ 2x + x2.
i. Show that f is a function. (Use the vertical line test for functions.)
ii. Find the domain and range of f.
iii. Find the x and y intercept(s) of f, if there are any.
iv. Show that ƒ is NOT one-to-one. (Give a counterexample.)
v. Find an interval I where f is one-to-one. Moreover, find the inverse of f
defined on I.
vi. Verify that f and f¯l are inverses of each other. (Hint: Use the composition
of functions.)
Transcribed Image Text:1. Consider the equation y = f(x) = V1+ 2x + x2. i. Show that f is a function. (Use the vertical line test for functions.) ii. Find the domain and range of f. iii. Find the x and y intercept(s) of f, if there are any. iv. Show that ƒ is NOT one-to-one. (Give a counterexample.) v. Find an interval I where f is one-to-one. Moreover, find the inverse of f defined on I. vi. Verify that f and f¯l are inverses of each other. (Hint: Use the composition of functions.)
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