Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015
1st Edition
ISBN: 9781680331165
Author: HOUGHTON MIFFLIN HARCOURT
Publisher: Houghton Mifflin Harcourt
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Question
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Chapter 4.5, Problem 59E
To determine

To solve: the equation f(x)=g(x) for the given function graphically and algebraically.

Expert Solution & Answer
Check Mark

Answer to Problem 59E

  x=1

Explanation of Solution

Given information:

Given functions are,

  f(x)=x3+x2x1

And

  g(x)=x+1

Calculation:

Consider the given functions.

  f(x)=x3+x2x1 …… (1)

  g(x)=x+1 …… (2)

Now, the points of intersection of the graph of f(x) and g(x) will be the solution of f(x)=g(x) .

Construct the graphs of f(x) and g(x) in same set of axes.

  Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 4.5, Problem 59E

Here, the point of intersection is (1,0) .

Thus, the solution is x=1 .

Now, solve f(x)=g(x) algebraically.

  x3+x2x1=x+1x3+x2x1+x1=0x3+x22=0x3x2+2x22=0x2(x1)+2(x1)=0(x1)(x2+2)=0

Now, x2+20 for any real x .

So, x1=0

Hence, x=1 is the only real solution of f(x)=g(x) .

Chapter 4 Solutions

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

Ch. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - Prob. 46ECh. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Prob. 53ECh. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - Prob. 56ECh. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - 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