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Chapter 1: Problem 57

Find the domain of the function. $$f(s)=\frac{\sqrt{s-1}}{s-4}$$

Short Answer

Expert verified
The domain of the function \(f(s)=\frac{\sqrt{s-1}}{s-4}\) is \([1, 4) \cup (4, +\infty)\).

Step by step solution

01

Identify Restrictions from Square Root

Firstly, note that \(s-1\) in the square root must be non-negative since the square root function is only defined for non-negative numbers. This means that: \(s-1 \geq 0\), which simplifies to: \(s \geq 1\).
02

Identify Restrictions from Fraction

Secondly, in order for the function to be defined, the denominator of the fraction (i.e., \(s-4\)) cannot be equal to 0. In other words, \(s \neq 4\).
03

Combine the Restrictions

Finally, combine the restrictions from the square root and the fraction. The combined domain of the function is all \(s\) such that \(s \geq 1\) and \(s \neq 4\). In interval notation this would be: \([1, 4) \cup (4, +\infty)\).

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