What is the domain for ax^(1/3) + b?

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In summary, the domain for the expression ax^(1/3) + b is the set of real numbers. This is because the cube root function is defined for all real numbers, unlike the square root function which is limited to non-negative numbers. Therefore, the domain for this expression is x > or = 0.
  • #1
mathdad
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Precalculus by David Cohen, 3rd Edition
Chapter 1, Section 1.3.
Question 3b.

Specify the domain.

ax^(1/3) + b

Solution:

x^(1/3) means the cube root of x.

Since there is a radical here, I will say the domain is the radicand > or = 0.

So, x > or = 0.

Yes?
 
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  • #2
RTCNTC said:
Precalculus by David Cohen, 3rd Edition
Chapter 1, Section 1.3.
Question 3b.

Specify the domain.

ax^(1/3) + b

Solution:

x^(1/3) means the cube root of x.

Since there is a radical here, I will say the domain is the radicand > or = 0.

So, x > or = 0.

Yes?

as cube root is defined for all real number (-ve number also) so the domain is set of real numbers
 
  • #3
You are right. I found the following definition online:

"The domain of a cube root function is the set of all real numbers. Unlike a square root function which is limited to nonnegative numbers, a cube root can use all real numbers because it is possible for three negatives to equal a negative."
 

Related to What is the domain for ax^(1/3) + b?

What is the "Find Domain" function used for?

The "Find Domain" function is used to determine the set of all possible input values, or independent variables, for a given mathematical function.

How do you find the domain of a function?

To find the domain of a function, you must first identify any restrictions on the input values. This could include restrictions such as division by zero or taking the square root of a negative number. Once these restrictions are identified, the domain is all real numbers that satisfy these restrictions.

Why is it important to find the domain of a function?

Finding the domain of a function is important because it allows you to understand the behavior of the function and make accurate predictions about its output. It also helps to identify any potential errors or undefined values.

What are some common mistakes when finding the domain of a function?

One common mistake is forgetting to consider restrictions such as square roots or logarithms, which can result in an incorrect domain. Another mistake is assuming that the domain is always all real numbers, when in fact there may be restrictions on the input values.

Can the domain of a function be negative?

Yes, the domain of a function can include negative numbers. It depends on the specific function and any restrictions that may be present. However, some functions may have a restricted domain that does not include negative numbers. It is important to carefully consider all restrictions when finding the domain of a function.

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