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1 Which of the following is not always true of a function and its inverse? A If f(a) = b, then f-1(b) = a. B They reflect across the line y = x. C (f f-1)(x) = x %3D D f-1(x) is a function.

1 Which of the following is not always true of a function and its inverse? A If f(a) = b, then f-1(b) = a. B They reflect across the line y = x. C (f f-1)(x) = x %3D D f-1(x) is a function.

Calculus: Early Transcendentals
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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1 Which of the following is not always true of a function and its inverse? A If f(a) = b, then f -1(b) = a. B They reflect across the line y = x. C (f f-1)(x) = x D f-1(x) is a function. 2 Which of the following best explains how you would prove that two functions, f(x) and g(x), are inverses of each other algebraically? F Use compositions of functions by solving f(g(x)) and g(f(x)). If the two compositions result in x, considering restrictions on domains, then the functions are inverses. G Graph the two functions to see if they appear to reflect across a line of symmetry.' H Make a table of values for f(x) and g(x) and compare them to see if the points are "flipped". Subtract g(x) from f(x). If the result is 0, then they are inverse functions.
Transcribed Image Text:1 Which of the following is not always true of a function and its inverse? A If f(a) = b, then f -1(b) = a. B They reflect across the line y = x. C (f f-1)(x) = x D f-1(x) is a function. 2 Which of the following best explains how you would prove that two functions, f(x) and g(x), are inverses of each other algebraically? F Use compositions of functions by solving f(g(x)) and g(f(x)). If the two compositions result in x, considering restrictions on domains, then the functions are inverses. G Graph the two functions to see if they appear to reflect across a line of symmetry.' H Make a table of values for f(x) and g(x) and compare them to see if the points are "flipped". Subtract g(x) from f(x). If the result is 0, then they are inverse functions.
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