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Chapter 1: Problem 14

Find the domain of each function. $$h(x)=\frac{5}{\frac{4}{x}-1}$$

Short Answer

Expert verified
The domain of the function is all real numbers except for x = 4.

Step by step solution

01

Identify the Indeterminate Form

Analyze the given function to locate the denominator that could potentially cause indeterminate form i.e., zero in the denominator. In this case, the denominator of our function is \(\frac{4}{x}-1\).
02

Set the Denominator Equal to Zero

For this exercise, set the denominator equal to zero and solve for x: \(\frac{4}{x}-1=0\).
03

Solve for x

Solve the equation \(\frac{4}{x}-1=0\) for x. First add 1 to both sides of the equation to get \(\frac{4}{x}=1\). Then multiply both sides with x to get 4 = x. Therefore, x = 4.
04

Determine the Excluded Value

We now found the value for which the function is undefined, namely x = 4. Thus, this value must be excluded from the domain.
05

Write the Domain

The domain of the function \(h(x)=\frac{5}{\frac{4}{x}-1}\) is all real numbers except for x = 4.

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