• Support PF! Buy your school textbooks, materials and every day products Here!

Square root of a function

  • Thread starter zaddyzad
  • Start date
  • #1
149
0

Homework Statement



I have the function H^2 + 12756H and I want to find the domain and range of it's square root algebraically.


Homework Equations




The Attempt at a Solution



I understand y= √(H^2 + 12756H) is undefined if H^2 + 12756H < 0, however I dont get how to find its domain and range using algebra. Maybe someone can help me.
 
Last edited:

Answers and Replies

  • #2
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,219
945

Homework Statement



I have the function H^2 + 12756H and I want to find the domain and range of it's square root algebraically.

Homework Equations



The Attempt at a Solution



I understand y= √(H^2 + 12756H) is undefined if H^2 + 12756H < 0, however I don't get how to find its domain and range using algebra. Maybe someone can help me.
Can you solve for H2 + 12756H = 0 ?

If you graph y = H2 + 12756H you get a continuous graph. H2 + 12756H cannot change sign without going through zero.

All of that should help you.
 
  • #3
149
0
I understand how to find the domain and range of the root function by looking at the original graph, however my question is can it be done algebraically, if so how?

And no I dont believe you can solve for H with 0 = h^2 + 12756h algebraically only with quadratic formula. The point of this post is to find out the easiest way to solve this sort of thing for domain, and would it be finding x-intercepts and deriving your domain of the root from that ?
 
Last edited:
  • #4
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
11,219
945
I understand how to find the domain and range of the root function by looking at the original graph, however my question is can it be done algebraically, if so how?

And no I don't believe you can solve for H with 0 = h^2 + 12756h algebraically only with quadratic formula. The point of this post is to find out the easiest way to solve this sort of thing for domain, and would it be finding x-intercepts and deriving your domain of the root from that ?
How purely algebraic do you want the solution to be?

Yes, it can be done!
 
  • #5
HallsofIvy
Science Advisor
Homework Helper
41,770
911

Homework Statement



I have the function H^2 + 12756H and I want to find the domain and range of it's square root algebraically.


Homework Equations




The Attempt at a Solution



I understand y= √(H^2 + 12756H) is undefined if H^2 + 12756H < 0, however I dont get how to find its domain and range using algebra. Maybe someone can help me.
H^2+ 12756H= H(H+ 12756)< 0 and the product of two numbers is negative if and only if the numbers are of opposite sign.
So either H< 0 and H+ 12756> or H> 0 and H+ 12756< 0.
(Only one of those is actually possible.)
 

Related Threads for: Square root of a function

Replies
3
Views
3K
  • Last Post
Replies
8
Views
1K
Replies
5
Views
9K
Replies
11
Views
3K
Replies
2
Views
2K
  • Last Post
Replies
5
Views
2K
Replies
5
Views
792
Replies
9
Views
1K
Top