MHB What is the domain for variables with cube roots?

[mathdad]

Specify the domain of each variable.

1. ax + b

Here x can be any integer.

In that case the domain is R, where R is ALL REAL NUMBERS.

2. ax^(1/3) + b

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

Let D = domain

x^(1/3) is > or = 0

[x^(1/3)]^3 > or = 0^(1/3)

x > or = 0

D = {x| x > or = 0}

Is any of this right?

 

[MarkFL]

Specify the domain of each variable.

1. ax + b

Here x can be any integer.

In that case the domain is R, where R is ALL REAL NUMBERS.

Correct, there would be no restriction we would need to impose on $x$.

2. ax^(1/3) + b

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

Let D = domain

x^(1/3) is > or = 0

[x^(1/3)]^3 > or = 0^(1/3)

x > or = 0

D = {x| x > or = 0}

Is any of this right?

Let's think about this...what is the cube of a negative number?

 

[mathdad]

Negative numbers can't have real number square roots, but negative numbers can have real number cube roots.

Sample: (-8)^(1/3) = -2

Back to my question.

(x)^(1/3) is the cube root of x. The domain can be any real number.