a. Answer The Domain: { R − ( − 3 , 4 ) } { All real number except − 3 a n d 4 } Explanation Given that: : f ( x ) = 3 x − 2 x 2 − x − 12 The domain of the function is defined as the function is real and defined for all set of input numbers except that makes the denominator zero Use the factor method for Denominator x 2 − x − 12 = 0 x 2 − ( 4 − 3 ) x − 12 = 0 x 2 − 4 x + 3 x − 12 = 0 x ( x − 4 ) + 3 ( x − 4 ) = 0 ( x + 3 ) ( x − 4 ) = 0 Now, apply zero product method to find the value of zeros of the given function x + 3 = x = − 3 Similarly x − 4 = 0 x = 4 x = 4 Hence, The Domain: { R − ( − 3 , 4 ) } { All real number except − 3 a n d 4 } b. To determine To find the zeros of f ( x ) = 3 x − 2 x 2 − x − 12 Answer The Zero at { 2 3 } Explanation Given that: : f ( x ) = 3 x − 2 x 2 − x − 12 The zeros of the function is defined as the function is real and defined for all set of input numbers except that makes the nominator zero. f ( x ) = 0 , if and only if when given numerator be 3 x − 2 = 0 Use the factor method for numerator and apply zero product method to find the value of zeros of the given function 3 x − 2 = 0 3 x = 2 x = 2 3 Hence, The Zero at { 2 3 }

Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Chapter 5, Problem 7CT

To determine

To find the domain of f(x)=3x−2x2−x−12

Expert Solution

Answer to Problem 7CT

The Domain: {R−(−3,4)}

{All real number except −3 and 4}

Explanation of Solution

Given that: : f(x)=3x−2x2−x−12

The domain of the function is defined as the function is real and defined for all set of input numbers except that makes the denominator zero

Use the factor method for Denominator

x2−x−12=0x2−(4−3)x−12=0x2−4x+3x−12=0x(x−4)+3(x−4)=0(x+3)(x−4)=0

Now, apply zero product method to find the value of zeros of the given function

x+3=x=−3

Similarly

x−4=0x=4x=4

Hence, The Domain: {R−(−3,4)}

{All real number except −3 and 4}

To determine

To find the zeros of f(x)=3x−2x2−x−12

Expert Solution

Answer to Problem 7CT

The Zero at {23}

Explanation of Solution

Given that: : f(x)=3x−2x2−x−12

The zeros of the function is defined as the function is real and defined for all set of input numbers except that makes the nominator zero.

f(x)=0, if and only if when given numerator be 3x−2=0

Use the factor method for numerator and apply zero product method to find the value of zeros of the given function

3x−2=03x=2x=23

Hence, The Zero at {23}

Chapter 5, Problem 6CT

Chapter 5, Problem 8CT

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

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Finding Local Maxima and Minima by Differentiation; Author: Professor Dave Explains;https://www.youtube.com/watch?v=pvLj1s7SOtk;License: Standard YouTube License, CC-BY

To find the domain of f ( x ) = 3 x − 2 x 2 − x − 12

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To find the domain of f(x)=3x−2x2−x−12

Answer to Problem 7CT

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To find the zeros of f(x)=3x−2x2−x−12

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Chapter 5 Solutions

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