Determine the Domain for 22(2/x - 1) = 30

22(2x1)=30 22(\frac{2}{x}-1)=30

What is the domain of the equation above?

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Step-by-step video solution

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00:00 Find the domain of substitution
00:03 Domain of substitution exists to ensure we don't divide by 0
00:07 Meaning the denominator in the fraction must be different from 0
00:11 We will use this formula in our exercise
00:16 This is the domain of substitution, and this is the solution to the question

Step-by-step written solution

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1

Understand the problem

22(2x1)=30 22(\frac{2}{x}-1)=30

What is the domain of the equation above?

2

Step-by-step solution

To find the domain of the given function 22(2x1)=30 22\left(\frac{2}{x} - 1\right) = 30 , follow these steps:

  • Identify critical terms: The term 2x\frac{2}{x} is undefined when x=0 x = 0 because division by zero is undefined.
  • We need to exclude x=0 x = 0 from the domain to ensure the function remains defined.
  • The correct domain for the equation is all real numbers except x=0 x = 0 .

Thus, the domain of the equation is x0 x \neq 0 .

Therefore, the solution to the problem is x0 x \neq 0 .

3

Final Answer

x≠0

Practice Quiz

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Select the the domain of the following fraction:

\( \frac{6}{x} \)

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