Precalculus: Mathematics for Calculus - 6th Edition
Precalculus: Mathematics for Calculus - 6th Edition
6th Edition
ISBN: 9780840068071
Author: Stewart, James, Redlin, Lothar, Watson, Saleem
Publisher: Cengage Learning
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In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …
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Chapter 2.1, Problem 25E
To determine

To evaluate f(x)=2|x−1| at a number, we substitute the number for x in the definition of f(x)

Expert Solution & Answer
Check Mark

Answer to Problem 25E

The values of the given function are:

  f(−2)=6,f(0)=2,f(12)=1,f(2)=2,f(x+1)=2|x|,f(x2+2)=2|x2+1|

Explanation of Solution

Given information: consider the function f(x)=2|x−1|

Calculation:

Evaluate the values of the function f(x)=2|x−1| for the given values of the variable x

Plug the value x=−2, in the function f(x)=2|x−1| then we get the value of f(−2).

  f(−2)=2|−2−1|f(−2)=2|−3|f(−2)=2(3)f(−2)=6

Plug the value x=0, in the function f(x)=2|x−1| then we get the value of f(0).

  f(0)=2|0−1|f(0)=2|−1|f(0)=2(1)f(0)=2

Plug the value x=12, in the function f(x)=2|x−1| then we get the value of f(12).

  f(12)=2|12−1|f(12)=2|−12|f(12)=2(12)f(12)=1

Plug the value x=2, in the function f(x)=2|x−1| then we get the value of f(2).

  f(2)=2|2−1|f(2)=2|1|f(2)=2

Plug the value x=x+1, in the function f(x)=2|x−1| then we get the value of f(x+1).

  f(x+1)=2|x+1−1|f(x+1)=2|x|

Plug the value x=x2+2, in the function f(x)=2|x−1| then we get the value of f(x2+2).

  f(x2+2)=2|x2+2−1|f(x2+2)=2|x2+1|

Thus, the values of the given function are:

  f(−2)=6,f(0)=2,f(12)=1,f(2)=2,f(x+1)=2|x|,f(x2+2)=2|x2+1|

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Chapter 2 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

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Prob. 31ECh. 2.4 - Prob. 32ECh. 2.4 - Prob. 33ECh. 2.5 - Fill in the blank with the appropriate direction...Ch. 2.5 - Prob. 2ECh. 2.5 - Prob. 3ECh. 2.5 - Prob. 4ECh. 2.5 - Prob. 5ECh. 2.5 - Prob. 6ECh. 2.5 - Prob. 7ECh. 2.5 - Prob. 8ECh. 2.5 - Prob. 9ECh. 2.5 - Prob. 10ECh. 2.5 - Prob. 11ECh. 2.5 - Prob. 12ECh. 2.5 - Prob. 13ECh. 2.5 - Prob. 14ECh. 2.5 - Prob. 15ECh. 2.5 - Prob. 16ECh. 2.5 - Prob. 17ECh. 2.5 - Prob. 18ECh. 2.5 - Prob. 19ECh. 2.5 - Prob. 20ECh. 2.5 - Prob. 21ECh. 2.5 - Prob. 22ECh. 2.5 - Prob. 23ECh. 2.5 - Prob. 24ECh. 2.5 - Prob. 25ECh. 2.5 - Prob. 26ECh. 2.5 - Prob. 27ECh. 2.5 - Prob. 28ECh. 2.5 - Prob. 29ECh. 2.5 - Prob. 30ECh. 2.5 - Prob. 31ECh. 2.5 - Prob. 32ECh. 2.5 - Prob. 33ECh. 2.5 - Prob. 34ECh. 2.5 - Prob. 35ECh. 2.5 - Prob. 36ECh. 2.5 - Prob. 37ECh. 2.5 - Prob. 38ECh. 2.5 - Prob. 39ECh. 2.5 - Prob. 40ECh. 2.5 - Prob. 41ECh. 2.5 - Prob. 42ECh. 2.5 - Prob. 43ECh. 2.5 - Prob. 44ECh. 2.5 - Prob. 45ECh. 2.5 - Prob. 46ECh. 2.5 - Prob. 47ECh. 2.5 - Prob. 48ECh. 2.5 - 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