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

  • Thread starter Thread starter mathdad
  • Start date Start date
  • Tags Tags
    Domain
AI Thread Summary
The discussion centers on determining the domain of the function ax^(1/3) + b. Initially, it is suggested that the domain is x ≥ 0 due to the presence of a radical. However, it is clarified that the cube root function is defined for all real numbers, meaning the domain encompasses all real numbers. This distinction is made to highlight that unlike square roots, cube roots can accept negative inputs. Ultimately, the correct domain for the function is confirmed to be all real numbers.
mathdad
Messages
1,280
Reaction score
0
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?
 
Last edited:
Mathematics news on Phys.org
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
 
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."
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Similar threads

MHB What is the domain for the expression 4/[(t - 1)•sqrt{t}]?
Replies
6
Views
2K
MHB What is the domain for variables with cube roots?
Replies
2
Views
1K
MHB Is 27 - (a - b)^3 a Difference of Cubes in Precalculus?
Replies
9
Views
2K
MHB Why is the domain of ax^(1/3) + b equal to all real numbers?
Replies
2
Views
1K
B Advice to obtain the domain of compound functions
Replies
2
Views
1K
MHB How do you factor a cubic function?
Replies
2
Views
2K
MHB How do I factor this expression: 3(x + 5)^3 + 2(x + 5)^2?
Replies
3
Views
1K
MHB How do you factor expressions like 3(x + h)^4 - 48(x + h)^2?
Replies
2
Views
1K
MHB What is the Domain of 1/x and 1/[(x - 1)(x + 2)(x - 3)]?
Replies
2
Views
1K
MHB What Is the Domain and Range of y=cos(3(x - 45°)) +2?
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top