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Find the domain of each function. $$g(x)=\frac{1}{\sqrt{x-3}}$$

Short Answer

Expert verified
The domain of the function \(g(x)=\frac{1}{\sqrt{x-3}}\) is \(x > 3\).

Step by step solution

01

Understanding the function

The function provided is \(g(x)=\frac{1}{\sqrt{x-3}}\). For this function to be defined: 1.The denominator must not be equal to zero. 2.The value inside the square root should be greater than or equal to zero.
02

Identifying the denominator and the root

In this case, the denominator of the function is \(\sqrt{x-3}\). Hence, this can't be equal to zero. So, \(x - 3 \neq 0\) or \(x \neq 3\). Additionally, the value inside the root should be greater than zero. So, \(x-3 > 0\) or \(x > 3\).
03

Conclusion: Identifying the domain

The domain of the function is \(x >3\). That is, all the values of x greater than 3.

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