Question

For each rational function, find the function values indicated, provided the value exists. $$ g(x)=\frac{2 x^{3}-x}{x^{2}-6 x+9} ;(\text { a ) } g(0) ;(\text { b) } g(-2) ;(\text { c) } g(3) $$

Name: Problem 14, Chapter 6: Intermediate Algebra : Concepts and Applications
Uploaded: 2020-07-13T03:29:36-08:00
Duration: 2 min 19 s
Channel: Ankit Gupta
Description: For each rational function, find the function values indicated, provided the value exists. g(x)=(2 x^3-x)/(x^2-6 x+9) ;( a ) g(0) ;( b) g(-2) ;( c) g(3)

   For each rational function, find the function values indicated, provided the value exists.
$$
g(x)=\frac{2 x^{3}-x}{x^{2}-6 x+9} ;(\text { a ) } g(0) ;(\text { b) } g(-2) ;(\text { c) } g(3)
$$

Intermediate Algebra : Concepts and Applications

Marvin L. Bittinger,… 10th Edition

Chapter 6, Problem 14

Instant Answer

Solved by Expert Ankit Gupta

07/13/2020

Step 1

Step 1: We are given the function $g(x)=\frac{2 x^{3}-x}{x^{2}-6 x+9}$ and we are asked to find the function values at $x=0$, $x=-2$, and $x=3$. Show more…

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For each rational function, find the function values indicated, provided the value exists. $$ g(x)=\frac{2 x^{3}-x}{x^{2}-6 x+9} ;(\text { a ) } g(0) ;(\text { b) } g(-2) ;(\text { c) } g(3) $$

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Key Concepts

Function Evaluation

Function evaluation means substituting a specific value for the variable in the function's expression and simplifying to obtain a result. This helps determine the output corresponding to particular inputs within the function's domain.

Rational Functions

A rational function is any function expressed as the quotient of two polynomials. It is important in algebra because its behavior is governed by both the numerator and the denominator, and evaluating it involves understanding how the polynomials interact.

Domain Restrictions

For rational functions, the domain is restricted by values that make the denominator zero, since division by zero is undefined. Prior to evaluation, it is essential to ensure that the input value does not lead to such a condition.

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