Contains the absolute value inequality formula foundation question, urgent! |f(x)|＜g(x) ==> -g(x)＜f(x)＜g(x) |F (x) | > G (x) = = > F (x) > G (x) or F (x) < - G (x) Is there any requirement for G (x) to make the above two formulas hold? The above two formulas hold when G (x) > 0 is mentioned in my reference book But when the teacher says and writes the topic, don't g (x) > 0, you can use the above formula If there is no requirement for G (x), can we write the derivation process of the above two formulas?

Contains the absolute value inequality formula foundation question, urgent! |f(x)|＜g(x) ==> -g(x)＜f(x)＜g(x) |F (x) | > G (x) = = > F (x) > G (x) or F (x) < - G (x) Is there any requirement for G (x) to make the above two formulas hold? The above two formulas hold when G (x) > 0 is mentioned in my reference book But when the teacher says and writes the topic, don't g (x) > 0, you can use the above formula If there is no requirement for G (x), can we write the derivation process of the above two formulas?

There is no need for G (x) > 0
When G (x) ≤ 0, the solution sets of | f (x) | < g (x) and - G (x) < f (x) < g (x) are empty sets, which are still equivalent. This does not need to be deduced, but is an extension of the conclusion. The second proposition can be understood in the same way