1. ## Modulus Functions

If a is positive, then $\displaystyle |f(x)|<a \Rightarrow -a<f(x)<a$.

Is this true if I change a to a function now? say $\displaystyle g(x)$

i.e. $\displaystyle |f(x)|<g(x) \Rightarrow -g(x)<f(x)<g(x)$ and I can just solve from here onwards?

Thanks a lot for those who can help!!!

2. Originally Posted by acc100jt
If a is positive, then $\displaystyle |f(x)|<a \Rightarrow -a<f(x)<a$.

Is this true if I change a to a function now? say $\displaystyle g(x)$

i.e. $\displaystyle |f(x)|<g(x) \Rightarrow -g(x)<f(x)<g(x)$ and I can just solve from here onwards?

Thanks a lot for those who can help!!!
Yes, I believe this must also be true.