2011-04-21, 06:04 PM
Branch up the funtion in different cases by considering when the argument for the absolute value is higher and lower than zero. Then analyze the resulting function.
The three intervals that derive from doing this are:
(-oo,0) ; [0,2/3) ; [2/3;+oo)
The function value on these intervals is, respectively:
sqrt(1+6x) ; sqrt(1) ; sqrt(5-6x)
This furthers restricts our domain for this funcion to:
[-1/6,0) ; [0,2/3) ; [2/3,5/6]
From there it's easy to see that the funcion will be limited between [0,1]
The three intervals that derive from doing this are:
(-oo,0) ; [0,2/3) ; [2/3;+oo)
The function value on these intervals is, respectively:
sqrt(1+6x) ; sqrt(1) ; sqrt(5-6x)
This furthers restricts our domain for this funcion to:
[-1/6,0) ; [0,2/3) ; [2/3,5/6]
From there it's easy to see that the funcion will be limited between [0,1]