What is the domain and range of y = 1/(x-1)(x+2)?

[sinjan.j]

Homework Statement

y = $$\frac{1}{(x-1)(x+2)}$$

find out the domain and range

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

$$x~E~R~-\{-2,1\}$$

The Attempt at a Solution

I know the solution and I used this methoD:

y(x^2 + x -2) =1 (where $$y\neq0$$ )

when x is real, the discriminant

y^2 -4y(-2y-1) >=0 (where $$y\neq0$$ )

9y^2 + 4y >= 0 (where $$y\neq0$$ )

y(9y +4) >= 0 (where $$y\neq0$$ )

y<= -4/9 or y>0


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

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[arunbg]

This is the simplest way that I know of. If graphing is simple enough, you can try.

 

[tiny-tim]

Welcome to PF!

Homework Statement

y = $$\frac{1}{(x-1)(x+2)}$$

find out the domain and range

Hi sinjan.j! Welcome to PF!

Easy method:

It looks nearly symmetric …

so adjust it to make it symmetric!

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.

 

[LordofDirT]

simpler method = calculator

 

[sinjan.j]

Thanx everbody

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