Homework Soursefind th domain of lnx36x25x122x22x12Solutionlnx36x25x122x22x
find th domain of: ln((x3+6x2+5x-12)/(-2x2-2x+12))
Solution
ln((x3+6x2+5x-12)/(-2x2-2x+12))
= ln[(x^3 +6x^2 +5x -12)/(-2x^2 -2x +12) ]
Undefined points : -2x^2 -2x +12
solve the quadratic equation we get : x= 2 ; x= -3
(x^3 +6x^2 +5x -12)/(-2x^2 -2x +12) >0
-(x+4)(x-1)/2(x-2) >0
(x+4)(x-1)/2(x-2) < 0
Solution for the inequality by computimg sign changes:
we get : x< -4 and 1<x<2
Combining all the conditions we get:
Domain: ( - inf , -4) U (1 , 2)
![find th domain of: ln((x3+6x2+5x-12)/(-2x2-2x+12))Solutionln((x3+6x2+5x-12)/(-2x2-2x+12)) = ln[(x^3 +6x^2 +5x -12)/(-2x^2 -2x +12) ] Undefined points : -2x^2 -2](/WebImages/19/find-th-domain-of-lnx36x25x122x22x12solutionlnx36x25x122x22x-1038729-1761539281-0.webp "find th domain of: ln((x3+6x2+5x-12)/(-2x2-2x+12))Solutionln((x3+6x2+5x-12)/(-2x2-2x+12)) = ln[(x^3 +6x^2 +5x -12)/(-2x^2 -2x +12) ] Undefined points : -2x^2 -2")
