Find out domain and range

  • Thread starter sinjan.j
  • Start date
  • #1
25
0

Homework Statement



y = [tex]\frac{1}{(x-1)(x+2)}[/tex]

find out the domain and range

ans: y<= -4/9 or y>0

[tex]x~E~R~-\{-2,1\}[/tex]





The Attempt at a Solution



I know the solution and I used this methoD:

y(x^2 + x -2) =1 (where [tex]y\neq0[/tex] )

when x is real, the discriminant

y^2 -4y(-2y-1) >=0 (where [tex]y\neq0[/tex] )

9y^2 + 4y >= 0 (where [tex]y\neq0[/tex] )

y(9y +4) >= 0 (where [tex]y\neq0[/tex] )

y<= -4/9 or y>0


My request is ... plz use some other easy method to illustrate this problem.. I want to know other methods of solving this same problem.. plz help.

====================================================================
Forum $ignature: www.lingouist.blogspot.com[/URL]
 
Last edited by a moderator:

Answers and Replies

  • #2
590
0
This is the simplest way that I know of. If graphing is simple enough, you can try.
 
  • #3
tiny-tim
Science Advisor
Homework Helper
25,832
251
Welcome to PF!

Homework Statement



y = [tex]\frac{1}{(x-1)(x+2)}[/tex]

find out the domain and range

Hi sinjan.j! Welcome to PF! :smile:

Easy method:

It looks nearly symmetric …

so adjust it to make it symmetric! :smile:

Hint: the range will be the same even if you make a substitution for x. Try w = x - a, where you choose a to make 1/(x-1)(x+2) symmetric in w.
 
  • #4
15
0
simpler method = calculator
 
  • #5
25
0
Thanx everbody

================================================== ==================
Forum $ignature: www.lingouist.blogspot.com[/URL]
 
Last edited by a moderator:

Related Threads on Find out domain and range

  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
7
Views
6K
  • Last Post
Replies
14
Views
2K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
4
Views
8K
Replies
2
Views
3K
Replies
2
Views
3K
  • Last Post
Replies
5
Views
1K
Top