I'm quite confused by the function y = |x^2 - 1|
I understand that y = x^2 - 1 when x^2 - 1 > 0 etc
But how do you solve it?
You get x^2 - 1 > 0
x^2 > 1
x > + or - 1
but it should be x<-1 and x>1
Is there some sort of inequation sign change when one of the sides is square rooted? Thanks in advance
I start here:
x^2-1 > 0. Factorize
(x+1)(x-1) > 0. > 0 means the product is positive. A product of 2 factors is positive if the factors have equal signs: (+) * (+) > 0 or (-) * (-) > 0. "+" means greater as zero, "-" means smaller as zero.
So your inequality becomes:
This method only works if you can factorize the term.Code:x+1 > 0 and x-1 > 0 or x+1 < 0 and x+1 < 0 x > -1 and x > 1 or x < -1 and x < -1 x > 1 or x < -1