Hellow mates.
Please help me finding the correct domain of the following function:
~~~~~√ (x^3 -2x^2 - 5x +6)
f(x)= ------------------------
~~~~~√(x^2 -x -2)
~~~~√(x^2 -x -6)(x -1)
f(x)= --------------------- Factoring the 3rd degree polynomial expression, using Ruffini´s algorithm.
~~~~~√(x^2 -x -2)
~~~~√(x -3)(x+2)(x -1)
f(x)= ----------------------- Factoring all polynomials.
~~~~√(x -2)(x +1)
Now we have to find the real sets of values of x.
(x +3)(x+2)(x -1)
------------------- >= 0
(x -2)(x +1)
Finally I get that x is positive in this intervals :
-∞ -2 -1 1 2 3 +∞
<---------------------------------------------------->
- + - + - +
Dom f(x)= )-2 , -1) U )1 , 2) U )3 , +∞)
I do not have the answer to this, but when I graph this function in GeoGebra, the function does not exists in )1 , 2), but only in the other two sets I get in my answer.
Can some one explain my error?
Please help me finding the correct domain of the following function:
~~~~~√ (x^3 -2x^2 - 5x +6)
f(x)= ------------------------
~~~~~√(x^2 -x -2)
~~~~√(x^2 -x -6)(x -1)
f(x)= --------------------- Factoring the 3rd degree polynomial expression, using Ruffini´s algorithm.
~~~~~√(x^2 -x -2)
~~~~√(x -3)(x+2)(x -1)
f(x)= ----------------------- Factoring all polynomials.
~~~~√(x -2)(x +1)
Now we have to find the real sets of values of x.
(x +3)(x+2)(x -1)
------------------- >= 0
(x -2)(x +1)
Finally I get that x is positive in this intervals :
-∞ -2 -1 1 2 3 +∞
<---------------------------------------------------->
- + - + - +
Dom f(x)= )-2 , -1) U )1 , 2) U )3 , +∞)
I do not have the answer to this, but when I graph this function in GeoGebra, the function does not exists in )1 , 2), but only in the other two sets I get in my answer.
Can some one explain my error?