Lookup tables are used quite often for work like that. They're small and fast.
But whether look-up or some formula, if the end result is an image file, and the format permits, it's best to save a color profile or at least the gamma value in the file for later viewing, rather than try adjusting RGB values yourself.
The reason: for typical byte-valued R, G, B channels, you have 256 unique values in each channel at each pixel. That's almost good enough to look good to the human eye (I wish "byte" had been defined as nine bits!) Any kind of math, aside from trivial value inversion, would map many-to-one for some of those values. The output won't have 256 values to pick from for each pixel for R, G, or B, but far fewer. That can lead to contouring, jaggies, color noise and other badness.
Precision issues aside, if any kind of decent quality is desired, all composting, mixing, blending, color correction, fake lens flare addition, chroma-keying and whatever, should be done in linear RGB space, where the values of R, G and B are in proportion to physical light intensity. The image math mimics physical light math. But where ultimate speed is vital, there are ways to cheat.