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

[mathdad]

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?

 

[kaliprasad]

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

 

[mathdad]

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."