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Chapter 3: Problem 77

What is the domain of the function \((3+x)^{1 / 4} ?\)

Short Answer

Expert verified
The domain of the function \(f(x) = (3+x)^{\frac{1}{4}}\) is all real numbers x such that \(x \geq -3\).

Step by step solution

01

Identify the Function and its Inner Expression

The given function is \(f(x) = (3+x)^{\frac{1}{4}}\). The expression inside the fourth root is \(3+x\).
02

Determine the Constraints on the Inner Expression

Since we are dealing with a fourth root, we know that the expression inside the root must be non-negative. That is, \(3+x \geq 0\).
03

Solve for the Domain

Now, we will solve the inequality \(3+x \geq 0\) to determine the valid values of x. 1. Subtract 3 from both sides of the inequality: \(x \geq -3\) So, the domain of the function \(f(x) = (3+x)^{\frac{1}{4}}\) includes all real numbers x such that \(x \geq -3\).

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