If you can change it into 1 by substitution, please do so, and then use the properties of composite function to find the range of inner function, that is, the definition range of outer function, and then it will be the same as 1.
For the periodic function, intercept a period, and then press 1 or 2 for processing.
Write the inverse of the original function. If the domain of the inverse function is easy to find, then we can directly find its maximum value.
When the above basic methods can't be used, surrender and seek the derivative (other methods to seek the maximum value, such as the combination of numbers and shapes, but according to experience, don't waste time trying in most cases, you have already guided the topic). Derive the derivative first, then write the zero and singularity of the derivative, and there are also endpoints. The largest is the maximum, and the smallest is the minimum. (Note, of course, that the singularity may correspond to infinitesimal or infinite, that is, there is neither minimum nor maximum. )