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Chapter 1: Problem 32

Determine the domain of the function represented by the given equation. $$f(x)=\frac{6}{x-5}$$

Short Answer

Expert verified
The domain of the function \(f(x)=\frac{6}{x-5}\) is all real numbers \(x\), excluding \(x = 5\).

Step by step solution

01

Identify the Denominator

In the function \(f(x)=\frac{6}{x-5}\), the denominator is \(x-5\). The function is undefined when the denominator is zero.
02

Set the Denominator Equal to Zero

To find the values that make the function undefined, equate the denominator, \(x-5\), to 0. Solve the equation \(x-5=0\) for x.
03

Obtain the Excluded Value

By solving the equation \(x-5=0\), we find that \(x = 5\), which is the value that makes the denominator zero and thus makes the function undefined.
04

Express the Domain

The domain of the function is all real numbers excluding the value that results in undefined output. In this case, \(x\) can be any real number except 5.

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Most popular questions from this chapter

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