MHB Why is the domain of ax^(1/3) + b equal to all real numbers?

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The function ax^(1/3) + b has a domain of all real numbers because the cube root function, x^(1/3), is defined for every real value of x. Regardless of the constants a and b, the output remains a real number for any real input. This characteristic ensures that the function does not encounter any restrictions or undefined values. Therefore, the domain is confirmed as the set of all real numbers, denoted as ℝ. Understanding this concept is crucial for analyzing similar functions in mathematics.
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Find the domain.

ax^(1/3) + b

I understand that a and b are constants here. I also know that x^(1/3) is equivalent to cube root{x}.

What I do not understand is why the answer is ALL REAL NUMBERS.
 
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It's "all real numbers" because no matter what real value you give x the function returns another real number. Given that a function's domain is defined wherever the function gives a real number for a real number input, ax^(/13) + b has the set $\mathbb{R}$ as its domain, i.e. it is defined for all real x.
 
Thanks. Good information.
 

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