Optimizing amplifier for specific frequency bands?

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Hi,
the question makes sense.
It is inherent in linear systems that 1mV input will give xmV output.
Raise the input to 2mV and out comes 2xmV and so on up the volume scale.
A wideband amp will keep this linearity across a wide frequency range as well as across the level range.

This law of linearity only breaks down when the amplifier becomes non linear eg when it clips or when the level becomes excessively contaminated by noise/distortion.
There are some circuits that deliberately become non linear with level and or frequency. FM radio gain adjustment, Dolby noise reduction and Dbx compressors are three more common examples.
 
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