How would you mathematically (rigorously) write down "where f(x) is max, g(x) is max. Therefore,

__range__ of g(x) is..." (same for

__domain__; I only got the solution, but how should one formalize the

**steps** to get the solution?)

Extra question: $\displaystyle f(x)>0 \Longleftrightarrow x\in(-\frac{5\pi}{4}+2k\pi, \frac{\pi}{4}+2k\pi)$ Is this 'right-to-left arrow' correctly put (is the sentence mathematically correct)? Or should there be only 'right arrow' ($\displaystyle \Longrightarrow$)? Or any other arrow

?