Question

Find the domain of the function. $$f(t)=\sqrt[3]{t-1}$$

   Find the domain of the function.
$$f(t)=\sqrt[3]{t-1}$$

College Algebra

College Algebra

James Stewart,… 7th Edition

Chapter 2, Problem 61

Instant Answer

Solved by Expert James Kiss

06/01/2020

Step 1

The cube root function is defined for all real numbers, so the only restriction on the domain is that the expression inside the cube root must be non-negative. Show more…

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Find the domain of the function. $$f(t)=\sqrt[3]{t-1}$$

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Key Concepts

Domain of a Function

The domain of a function is the set of all input values for which the function produces a valid output. When determining the domain, one must consider the operations performed in the function and the restrictions they impose, such as division by zero or taking even roots of negative numbers.

Cube Root Function

A cube root function involves finding the cube root of a number, which means the operation is the inverse of raising a number to the third power. Unlike square roots, cube roots are defined for all real numbers, including both positive and negative values, because every real number has a unique cube root.

Radical Functions with Odd Indices

Radical functions where the radical has an odd index, like the cube root, do not have the same restrictions as those with an even index. This is because odd-index radicals are defined for all real numbers, ensuring that the expression under the radical can be any real number without leading to undefined conditions.

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