Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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Question

Chapter 2.3, Problem 9QR

To determine

To find:The solution of equation f(x)=4 for f(x)={5−x, x≤3−x2+6x−8, x>3 .

Expert Solution & Answer

Answer to Problem 9QR

The solution of equation f(x)=4 for f(x)={5−x, x≤3−x2+6x−8, x>3 is x=1 .

Explanation of Solution

Given information:The functionis f(x)={5−x, x≤3−x2+6x−8, x>3 .

Calculation:

Find the value of the equation for f(x)=5−x if x≤3 .

f(x)=45−x=4x=5−4x=1

So, the solution of the equation f(x)=4 is x=1 .

Now, solve the equation for the function f(x)=−x2+6x−8 if x>3 .

f(x)=4−x2+6x−8=4x2−6x+12=0

Calculate the discriminant of the above equation.

b2−4ac=(−6)2−4(1)(12)=36−48=−12

The discriminant of the equation is negative. So, the solution is not possible for any real value of x .

Therefore, the solution of equation f(x)=4 for f(x)={5−x, x≤3−x2+6x−8, x>3 is x=1 .

Chapter 2.3, Problem 8QR

Chapter 2.3, Problem 10QR

Chapter 2 Solutions

Calculus: Graphical, Numerical, Algebraic

Ch. 2.1 - Prob. 1QR Ch. 2.1 - Prob. 2QR Ch. 2.1 - Prob. 3QR Ch. 2.1 - Prob. 4QR Ch. 2.1 - Prob. 5QR Ch. 2.1 - Prob. 6QR Ch. 2.1 - Prob. 7QR Ch. 2.1 - Prob. 8QR Ch. 2.1 - Prob. 9QR Ch. 2.1 - Prob. 10QR

Ch. 2.1 - Prob. 1E Ch. 2.1 - Prob. 2E Ch. 2.1 - Prob. 3E Ch. 2.1 - Prob. 4E Ch. 2.1 - Prob. 5E Ch. 2.1 - Prob. 6E Ch. 2.1 - Prob. 7E Ch. 2.1 - Prob. 8E Ch. 2.1 - Prob. 9E Ch. 2.1 - Prob. 10E Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - Prob. 36E Ch. 2.1 - Prob. 37E Ch. 2.1 - Prob. 38E Ch. 2.1 - Prob. 39E Ch. 2.1 - Prob. 40E Ch. 2.1 - Prob. 41E Ch. 2.1 - Prob. 42E Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - Prob. 45E Ch. 2.1 - Prob. 46E Ch. 2.1 - Prob. 47E Ch. 2.1 - Prob. 48E Ch. 2.1 - Prob. 49E Ch. 2.1 - Prob. 50E Ch. 2.1 - 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The solution of equation f ( x ) = 4 for f ( x ) = { 5 − x , x ≤ 3 − x 2 + 6 x − 8 , x &gt; 3 .