Math Problem Statement
What is the domain and range of(2x^5-1)^1/3
Solution
To determine the domain and range of the function , let's break it down step by step:
Domain
The domain of a function refers to all the values of for which the function is defined.
For the function , note that:
- The expression can take any real value, because polynomials (like ) are defined for all real .
- The cube root function is defined for all real numbers, including both positive and negative values.
Thus, there are no restrictions on . Therefore, the domain of is:
Range
The range of a function refers to all the possible output values (i.e., values of ).
- The expression can take any real value, as the term grows without bound as increases or decreases.
- The cube root of any real number is also a real number, which means that can also take any real value.
Thus, the range of is also:
Summary
- Domain: (all real numbers)
- Range: (all real numbers)
Would you like further details or have any questions?
Here are 5 related questions:
- What is the domain and range of ?
- How do you find the range of a function given its graph?
- What is the inverse of ?
- What happens to the domain when dealing with even roots?
- How do you solve equations involving cube roots?
Tip: Cube root functions are defined for all real numbers, unlike square roots which are limited to non-negative numbers.
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Math Problem Analysis
Mathematical Concepts
Algebra
Functions
Domain and Range
Cube Roots
Formulas
f(x) = (2x^5 - 1)^(1/3)
Theorems
Domain of Polynomials
Properties of Cube Roots
Suitable Grade Level
Grades 10-12