Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
1st Edition
ISBN: 9780078682278
Author: McGraw-Hill, Berchie Holliday
Publisher: Glencoe/McGraw-Hill
bartleby

Concept explainers

bartleby

Videos

Question
Book Icon
Chapter 1.2, Problem 32E
To determine

To find: f(12) .

Expert Solution & Answer
Check Mark

Answer to Problem 32E

  12

Explanation of Solution

Given information: g(x)=1x2[fg][x]=x4+x21+x2 

Calculation:

Since, [fg][x]=f(g(x))

Therefore, x4+x21+x2=f(g(x))

To find f(12) , we have to guess the numerator and denominator f(x) .

Let’s assume the denominator to be (1+x) . Plug g(x) in and we get,

  1+(1x2)=2x2

This value is not equal to the denominator of [fg][x] .

Let’s assume the denominator to be (1x) . Plug g(x) in and we get,

  1(1x2)=x2

This value is not equal to the denominator of [fg][x] .

Let’s assume the denominator to be (2x) . Plug g(x) in and we get,

  2(1x2)=1x2

Since, this value is equal to the denominator of [fg][x] . Thus, the denominator of f(x) is 2x .

Similarly, numerator of f(x) can be determined.

Let’s assume the numerator to be (1+x) . Plug g(x) in and we get,

  1+(1x2)=2x2

This value is not equal to the numeratorof [fg][x] .

Let’s assume the numeratorto be x2 to get the power 4. Plug g(x) in and we get,

  (1x2)4=12x2+x4

This value is not equal to the numeratorof [fg][x] .

Let’s assume the numeratorto be (x2+3x) to get 3x. Plug g(x) in and we get,

  (1x2)2+3(1x2)=12x2+x4+33x2=x45x2+4

This value is not equal to the numeratorof [fg][x] .

Let’s assume the numeratorto be (x23x) to reverse the sign. Plug g(x) in and we get,

  (1x2)23(1x2)=12x2+x43+3x2=x4+x22

This value is not equal to the numeratorof [fg][x] .

Let’s assume the numeratorto be (x23x+2) to remove +2. Plug g(x) in and we get,

  (1x2)23(1x2)+2=12x2+x43+3x2+2=x4+x2

Since, this value is equal to the numeratorof [fg][x] . Thus, the numerator of f(x) is x23x+2 .

So, the function f(x) can be written as follows:

  f(x)=x23x+22x

Put x=12 in the above function, and evaluate f(12) as shown below.

  f(12)=(12)23(12)+22(12)=(14)(32)+22(12)=(14)(64)+(84)(42)(12)=(34)(32)=12

Therefore, f(12) is 12 .

Chapter 1 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 1.1 - Prob. 11CFUCh. 1.1 - Prob. 12CFUCh. 1.1 - Prob. 13CFUCh. 1.1 - Prob. 14CFUCh. 1.1 - Prob. 15CFUCh. 1.1 - Prob. 16CFUCh. 1.1 - Prob. 17ECh. 1.1 - Prob. 18ECh. 1.1 - Prob. 19ECh. 1.1 - Prob. 20ECh. 1.1 - Prob. 21ECh. 1.1 - Prob. 22ECh. 1.1 - Prob. 23ECh. 1.1 - Prob. 24ECh. 1.1 - Prob. 25ECh. 1.1 - Prob. 26ECh. 1.1 - Prob. 27ECh. 1.1 - Prob. 28ECh. 1.1 - Prob. 29ECh. 1.1 - Prob. 30ECh. 1.1 - Prob. 31ECh. 1.1 - Prob. 32ECh. 1.1 - Prob. 33ECh. 1.1 - Prob. 34ECh. 1.1 - Prob. 35ECh. 1.1 - Prob. 36ECh. 1.1 - Prob. 37ECh. 1.1 - Prob. 38ECh. 1.1 - Prob. 39ECh. 1.1 - Prob. 40ECh. 1.1 - Prob. 41ECh. 1.1 - Prob. 42ECh. 1.1 - Prob. 43ECh. 1.1 - Prob. 44ECh. 1.1 - Prob. 45ECh. 1.1 - Prob. 46ECh. 1.1 - Prob. 47ECh. 1.1 - Prob. 48ECh. 1.1 - Prob. 49ECh. 1.1 - Prob. 50ECh. 1.1 - Prob. 51ECh. 1.1 - Prob. 52ECh. 1.1 - Prob. 53ECh. 1.1 - Prob. 54ECh. 1.1 - Prob. 55ECh. 1.1 - Prob. 56ECh. 1.1 - Prob. 57ECh. 1.2 - Prob. 1GCECh. 1.2 - Prob. 2GCECh. 1.2 - Prob. 3GCECh. 1.2 - Prob. 4GCECh. 1.2 - Prob. 5GCECh. 1.2 - Prob. 1CFUCh. 1.2 - Prob. 2CFUCh. 1.2 - Prob. 3CFUCh. 1.2 - Prob. 4CFUCh. 1.2 - Prob. 5CFUCh. 1.2 - Prob. 6CFUCh. 1.2 - Prob. 7CFUCh. 1.2 - Prob. 8CFUCh. 1.2 - Prob. 9CFUCh. 1.2 - Prob. 10CFUCh. 1.2 - Prob. 11ECh. 1.2 - Prob. 12ECh. 1.2 - Prob. 13ECh. 1.2 - Prob. 14ECh. 1.2 - Prob. 15ECh. 1.2 - Prob. 16ECh. 1.2 - Prob. 17ECh. 1.2 - Prob. 18ECh. 1.2 - Prob. 19ECh. 1.2 - Prob. 20ECh. 1.2 - Prob. 21ECh. 1.2 - Prob. 22ECh. 1.2 - Prob. 23ECh. 1.2 - Prob. 24ECh. 1.2 - Prob. 25ECh. 1.2 - Prob. 26ECh. 1.2 - Prob. 27ECh. 1.2 - Prob. 28ECh. 1.2 - Prob. 29ECh. 1.2 - Prob. 30ECh. 1.2 - Prob. 31ECh. 1.2 - Prob. 32ECh. 1.2 - Prob. 33ECh. 1.2 - Prob. 34ECh. 1.2 - Prob. 35ECh. 1.2 - Prob. 36ECh. 1.2 - Prob. 37ECh. 1.2 - Prob. 38ECh. 1.2 - Prob. 39ECh. 1.3 - Prob. 1CFUCh. 1.3 - Prob. 2CFUCh. 1.3 - Prob. 3CFUCh. 1.3 - Prob. 4CFUCh. 1.3 - Prob. 5CFUCh. 1.3 - Prob. 6CFUCh. 1.3 - Prob. 7CFUCh. 1.3 - Prob. 8CFUCh. 1.3 - Prob. 9CFUCh. 1.3 - Prob. 10CFUCh. 1.3 - Prob. 11CFUCh. 1.3 - Prob. 12ECh. 1.3 - Prob. 13ECh. 1.3 - Prob. 14ECh. 1.3 - Prob. 15ECh. 1.3 - Prob. 16ECh. 1.3 - Prob. 17ECh. 1.3 - Prob. 18ECh. 1.3 - Prob. 19ECh. 1.3 - Prob. 20ECh. 1.3 - Prob. 21ECh. 1.3 - Prob. 22ECh. 1.3 - Prob. 23ECh. 1.3 - Prob. 24ECh. 1.3 - Prob. 25ECh. 1.3 - Prob. 26ECh. 1.3 - Prob. 27ECh. 1.3 - Prob. 28ECh. 1.3 - Prob. 29ECh. 1.3 - Prob. 30ECh. 1.3 - Prob. 31ECh. 1.3 - Prob. 32ECh. 1.3 - Prob. 33ECh. 1.3 - Prob. 34ECh. 1.3 - Prob. 35ECh. 1.3 - Prob. 36ECh. 1.3 - Prob. 37ECh. 1.3 - Prob. 38ECh. 1.3 - Prob. 39ECh. 1.3 - Prob. 40ECh. 1.3 - Prob. 41ECh. 1.3 - Prob. 42ECh. 1.3 - Prob. 43ECh. 1.3 - Prob. 44ECh. 1.3 - Prob. 45ECh. 1.3 - Prob. 46ECh. 1.3B - Prob. 1GCECh. 1.3B - Prob. 2GCECh. 1.3B - Prob. 3GCECh. 1.4 - Prob. 1CFUCh. 1.4 - Prob. 2CFUCh. 1.4 - Prob. 3CFUCh. 1.4 - Prob. 4CFUCh. 1.4 - Prob. 5CFUCh. 1.4 - Prob. 6CFUCh. 1.4 - Prob. 7CFUCh. 1.4 - Prob. 8CFUCh. 1.4 - Prob. 9CFUCh. 1.4 - Prob. 10CFUCh. 1.4 - Prob. 11ECh. 1.4 - Prob. 12ECh. 1.4 - Prob. 13ECh. 1.4 - Prob. 14ECh. 1.4 - Prob. 15ECh. 1.4 - Prob. 16ECh. 1.4 - Prob. 17ECh. 1.4 - Prob. 18ECh. 1.4 - Prob. 19ECh. 1.4 - Prob. 20ECh. 1.4 - Prob. 21ECh. 1.4 - Prob. 22ECh. 1.4 - Prob. 23ECh. 1.4 - Prob. 24ECh. 1.4 - Prob. 25ECh. 1.4 - Prob. 26ECh. 1.4 - Prob. 27ECh. 1.4 - Prob. 28ECh. 1.4 - Prob. 29ECh. 1.4 - Prob. 30ECh. 1.4 - Prob. 31ECh. 1.4 - Prob. 32ECh. 1.4 - Prob. 33ECh. 1.4 - Prob. 34ECh. 1.4 - Prob. 35ECh. 1.4 - Prob. 1MCQCh. 1.4 - Prob. 2MCQCh. 1.4 - Prob. 3MCQCh. 1.4 - Prob. 4MCQCh. 1.4 - Prob. 5MCQCh. 1.4 - Prob. 6MCQCh. 1.4 - Prob. 7MCQCh. 1.4 - Prob. 8MCQCh. 1.4 - Prob. 9MCQCh. 1.4 - Prob. 10MCQCh. 1.5 - Prob. 1CFUCh. 1.5 - Prob. 2CFUCh. 1.5 - Prob. 3CFUCh. 1.5 - Prob. 4CFUCh. 1.5 - Prob. 5CFUCh. 1.5 - Prob. 6CFUCh. 1.5 - Prob. 7CFUCh. 1.5 - Prob. 8CFUCh. 1.5 - Prob. 9CFUCh. 1.5 - Prob. 10CFUCh. 1.5 - Prob. 11CFUCh. 1.5 - Prob. 12ECh. 1.5 - Prob. 13ECh. 1.5 - Prob. 14ECh. 1.5 - Prob. 15ECh. 1.5 - Prob. 16ECh. 1.5 - Prob. 17ECh. 1.5 - Prob. 18ECh. 1.5 - Prob. 19ECh. 1.5 - Prob. 20ECh. 1.5 - Prob. 21ECh. 1.5 - Prob. 22ECh. 1.5 - Prob. 23ECh. 1.5 - Prob. 24ECh. 1.5 - Prob. 25ECh. 1.5 - Prob. 26ECh. 1.5 - Prob. 27ECh. 1.5 - Prob. 28ECh. 1.5 - Prob. 29ECh. 1.5 - Prob. 30ECh. 1.5 - Prob. 31ECh. 1.5 - Prob. 32ECh. 1.5 - Prob. 33ECh. 1.5 - Prob. 34ECh. 1.5 - Prob. 35ECh. 1.5 - Prob. 36ECh. 1.5 - Prob. 37ECh. 1.5 - Prob. 38ECh. 1.5 - Prob. 39ECh. 1.5 - Prob. 40ECh. 1.6 - Prob. 1CFUCh. 1.6 - Prob. 2CFUCh. 1.6 - Prob. 3CFUCh. 1.6 - Prob. 4CFUCh. 1.6 - Prob. 5CFUCh. 1.6 - Prob. 6ECh. 1.6 - Prob. 7ECh. 1.6 - Prob. 8ECh. 1.6 - Prob. 9ECh. 1.6 - Prob. 10ECh. 1.6 - Prob. 11ECh. 1.6 - Prob. 12ECh. 1.6 - Prob. 13ECh. 1.6 - Prob. 14ECh. 1.6 - Prob. 15ECh. 1.6 - Prob. 16ECh. 1.6 - Prob. 17ECh. 1.6 - Prob. 18ECh. 1.6 - Prob. 19ECh. 1.7 - Prob. 1CFUCh. 1.7 - Prob. 2CFUCh. 1.7 - Prob. 3CFUCh. 1.7 - Prob. 4CFUCh. 1.7 - Prob. 5CFUCh. 1.7 - Prob. 6CFUCh. 1.7 - Prob. 7CFUCh. 1.7 - Prob. 8CFUCh. 1.7 - Prob. 9CFUCh. 1.7 - Prob. 10CFUCh. 1.7 - Prob. 11ECh. 1.7 - Prob. 12ECh. 1.7 - Prob. 13ECh. 1.7 - Prob. 14ECh. 1.7 - Prob. 15ECh. 1.7 - Prob. 16ECh. 1.7 - Prob. 17ECh. 1.7 - Prob. 18ECh. 1.7 - Prob. 19ECh. 1.7 - Prob. 20ECh. 1.7 - Prob. 21ECh. 1.7 - Prob. 22ECh. 1.7 - Prob. 23ECh. 1.7 - Prob. 24ECh. 1.7 - Prob. 25ECh. 1.7 - Prob. 26ECh. 1.7 - Prob. 27ECh. 1.7 - Prob. 28ECh. 1.7 - Prob. 29ECh. 1.7 - Prob. 30ECh. 1.7 - Prob. 31ECh. 1.7 - Prob. 32ECh. 1.7 - Prob. 33ECh. 1.7 - Prob. 34ECh. 1.7 - Prob. 35ECh. 1.7 - Prob. 36ECh. 1.7 - Prob. 37ECh. 1.8 - Prob. 1CFUCh. 1.8 - Prob. 2CFUCh. 1.8 - Prob. 3CFUCh. 1.8 - Prob. 4CFUCh. 1.8 - Prob. 5CFUCh. 1.8 - Prob. 6CFUCh. 1.8 - Prob. 7CFUCh. 1.8 - Prob. 8CFUCh. 1.8 - Prob. 9ECh. 1.8 - Prob. 10ECh. 1.8 - Prob. 11ECh. 1.8 - Prob. 12ECh. 1.8 - Prob. 13ECh. 1.8 - Prob. 14ECh. 1.8 - Prob. 15ECh. 1.8 - Prob. 16ECh. 1.8 - Prob. 17ECh. 1.8 - Prob. 18ECh. 1.8 - Prob. 19ECh. 1.8 - Prob. 20ECh. 1.8 - Prob. 21ECh. 1.8 - Prob. 22ECh. 1.8 - Prob. 23ECh. 1.8 - Prob. 24ECh. 1.8 - Prob. 25ECh. 1.8 - Prob. 26ECh. 1.8 - Prob. 27ECh. 1.8 - Prob. 28ECh. 1.8 - Prob. 29ECh. 1.8 - Prob. 30ECh. 1.8 - Prob. 31ECh. 1.8 - Prob. 32ECh. 1 - Prob. 1SGACh. 1 - Prob. 2SGACh. 1 - Prob. 3SGACh. 1 - Prob. 4SGACh. 1 - Prob. 5SGACh. 1 - Prob. 6SGACh. 1 - Prob. 7SGACh. 1 - Prob. 8SGACh. 1 - Prob. 9SGACh. 1 - Prob. 10SGACh. 1 - Prob. 11SGACh. 1 - Prob. 12SGACh. 1 - Prob. 13SGACh. 1 - Prob. 14SGACh. 1 - Prob. 15SGACh. 1 - Prob. 16SGACh. 1 - Prob. 17SGACh. 1 - Prob. 18SGACh. 1 - Prob. 19SGACh. 1 - Prob. 20SGACh. 1 - Prob. 21SGACh. 1 - Prob. 22SGACh. 1 - Prob. 23SGACh. 1 - Prob. 24SGACh. 1 - Prob. 25SGACh. 1 - Prob. 26SGACh. 1 - Prob. 27SGACh. 1 - Prob. 28SGACh. 1 - Prob. 29SGACh. 1 - Prob. 30SGACh. 1 - Prob. 31SGACh. 1 - Prob. 32SGACh. 1 - Prob. 33SGACh. 1 - Prob. 34SGACh. 1 - Prob. 35SGACh. 1 - Prob. 36SGACh. 1 - Prob. 37SGACh. 1 - Prob. 38SGACh. 1 - Prob. 39SGACh. 1 - Prob. 40SGACh. 1 - Prob. 41SGACh. 1 - Prob. 42SGACh. 1 - Prob. 43SGACh. 1 - Prob. 44SGACh. 1 - Prob. 45SGACh. 1 - Prob. 46SGACh. 1 - Prob. 47SGACh. 1 - Prob. 48SGACh. 1 - Prob. 49SGACh. 1 - Prob. 50SGACh. 1 - Prob. 51SGACh. 1 - Prob. 52SGACh. 1 - Prob. 53SGACh. 1 - Prob. 54SGACh. 1 - Prob. 55SGACh. 1 - Prob. 56SGACh. 1 - Prob. 57SGACh. 1 - Prob. 58SGACh. 1 - Prob. 59SGACh. 1 - Prob. 60SGACh. 1 - Prob. 61SGACh. 1 - Prob. 62SGACh. 1 - Prob. 63SGACh. 1 - Prob. 64SGACh. 1 - Prob. 65SGACh. 1 - Prob. 66SGACh. 1 - Prob. 67SGACh. 1 - Prob. 68SGACh. 1 - Prob. 69SGACh. 1 - Prob. 1SAPCh. 1 - Prob. 2SAPCh. 1 - Prob. 3SAPCh. 1 - Prob. 4SAPCh. 1 - Prob. 5SAPCh. 1 - Prob. 6SAPCh. 1 - Prob. 7SAPCh. 1 - Prob. 8SAPCh. 1 - Prob. 9SAPCh. 1 - Prob. 10SAP

Additional Math Textbook Solutions

Find more solutions based on key concepts
Knowledge Booster
Background pattern image
Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Text book image
Calculus: Early Transcendentals
Calculus
ISBN:9781285741550
Author:James Stewart
Publisher:Cengage Learning
Text book image
Thomas' Calculus (14th Edition)
Calculus
ISBN:9780134438986
Author:Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:PEARSON
Text book image
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:9780134763644
Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON
Text book image
Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman
Text book image
Precalculus
Calculus
ISBN:9780135189405
Author:Michael Sullivan
Publisher:PEARSON
Text book image
Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning
Limits and Continuity; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9brk313DjV8;License: Standard YouTube License, CC-BY