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Chapter 1: Problem 59

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

Short Answer

Expert verified
The domain of the function \(f(x)=\frac{x-4}{\sqrt{x}}\) is \(x>0\).

Step by step solution

01

Find Values for Which the Function is Defined

Since there's a square root in the denominator of the function, the square root must be defined and not equal to zero (since we can't divide by zero). This means we must find the set of all \(x\) that make \(x >= 0\). In other words, since we are taking the square root of \(x\) in the denominator, \(x\) must be a non-negative number. However, \(x\) cannot be 0, because that would lead to division by zero in the denominator.
02

Consider the Numerator

For the numerator, it can take on any value, so we don't have any restrictions on \(x\) from the numerator.
03

Combine the Restrictions

The domain of the function is the set of all \(x\) for which the function is defined. In this case, it's all the real numbers greater than 0. So the required domain of \(f(x)\) is \(x>0\).

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Most popular questions from this chapter

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