Question no 1 part f shouldn't be the domain be (-infinity,-2] union [6,infinity] instead of given answer
I am getting |x| belongs to (-infinity, -2] U [6, infinity). Since, mod x can't be negative we get.
|x| belongs to [6, infinity) or x belongs to (insert the given answer here).
Ya it means I am right the answer key is wrong
No, the answer key is correct. Domain is the set of values of x and not |x|, so x belongs to (-infinity, -6] U [6, infinity).
Why in example 1.95 and 1.98 third log term is eliminated while finding domain of function
For log base 10 to be defined, its argument should be greater than zero. That's what the step is done.
The argument is made greater than zero.