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Chapter 2: Problem 19

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

Short Answer

Expert verified
The domain of the function \(g(x)\) is (3, +\(\infty\)).

Step by step solution

01

Identify the restrictions

First, recognize that \(x-3\) must be greater than 0 because it is under the square root and we cannot take a square root of a negative number. Secondly, since it is in the denominator, it cannot be equal to 0 because division by zero is undefined. Therefore, the inequality to solve is \(x-3 > 0\).
02

Solve the inequality

Solve the inequality by adding 3 to both sides: \(x > 3\).
03

Write the domain

The domain of the function \(g(x)\) is all real numbers greater than 3. In interval notation, this is represented as (3, +\(\infty\)).

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