Question

Let $f(x)=x+3$ and $g(x)=x^{2}-9$. Determine $(f / g)(3)$.

Name: Problem 111, Chapter 4: Intermediate Algebra for College Students
Uploaded: 2021-07-09T19:29:40-08:00
Duration: 1 min 34 s
Channel: Lewis Groves
Description: Let f(x)=x+3 and g(x)=x^2-9. Determine (f / g)(3).

   Let $f(x)=x+3$ and $g(x)=x^{2}-9$. Determine $(f / g)(3)$.

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 4, Problem 111

Instant Answer

Solved by Expert Lewis Groves

07/09/2021

Step 1

So, (f/g)(x) = (x+3) / (x^2 - 9). Show more…

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Let $f(x)=x+3$ and $g(x)=x^{2}-9$. Determine $(f / g)(3)$.

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Key Concepts

Domain Restrictions for Rational Functions

When dealing with the division of functions, it is crucial to ensure that the denominator is not equal to zero, as this would make the expression undefined. Recognizing and identifying values that cause the denominator to vanish helps in determining the valid input values for the quotient function.

Function Evaluation

This concept involves substituting a specific value into a function to calculate its output. In problems like this, each function is evaluated at a particular point, which is essential for determining their respective outputs before performing further operations.

Division of Functions

The division of functions entails creating a new function defined as the quotient of two functions, expressed as (f/g)(x) = f(x)/g(x). Understanding this operation is critical when combining functions and analyzing how their individual outputs interact.

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