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Chapter 1: Problem 54

Find the domain of the function. $$f(t)=\sqrt[3]{t+4}$$

Short Answer

Expert verified
The domain of the function \(f(t)=\sqrt[3]{t+4}\) is all real numbers, or \((-鈭�, 鈭�)\) in interval notation.

Step by step solution

01

Understand the Function

The function provided is a cube root function, and it is given by: \(f(t)=\sqrt[3]{t+4}\). As for cube root functions, they are defined for all real numbers, it means that the value inside the cube root can be any real number.
02

Identify the Domain

In this function, the domain encompasses values for \(t\) which make the expression \(t+4\) valid. But since, in this case, the operation is a cube root which allows all real numbers, including negatives, the domain of this function is the set of all real numbers.
03

Write Down the Domain in Interval Notation

Since the cube root function permits all real numbers, the domain of the function is all real numbers, denoted as \((-鈭�, 鈭�)\) in interval notation.

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