Question

Determine the domain of each function. $$ f(x)=\frac{x-4}{x-5} $$

Name: Problem 17, Chapter 6: Intermediate Algebra for College Students
Uploaded: 2020-07-07T17:25:27-08:00
Duration: 1 min 3 s
Channel: Alexandra Ali
Description: Determine the domain of each function. f(x)=(x-4)/(x-5)

   Determine the domain of each function.
$$
f(x)=\frac{x-4}{x-5}
$$

Intermediate Algebra for College Students

Allen R. Angel;… 10th Edition

Chapter 6, Problem 17

Instant Answer

Solved by Expert Alexandra Ali

07/07/2020

Step 1

In this case, the denominator is (x-5). Setting it equal to zero, we get: x - 5 = 0 x = 5 So, x = 5 would make the denominator equal to zero. Show more…

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Determine the domain of each function. $$ f(x)=\frac{x-4}{x-5} $$

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Key Concepts

Domain

The domain of a function consists of all input values for which the function yields a valid output. In determining the domain, one must identify and exclude any values that cause the function to become undefined, such as those that result in division by zero or produce negative values under an even root in the case of real-valued functions.

Rational Functions

Rational functions are functions expressed as the ratio of two polynomials. The key aspect when analyzing the domain of a rational function is to ensure that the denominator is never zero, as division by zero is undefined. This involves setting the denominator unequal to zero and solving for the input values that need to be excluded.

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