What is a complex function?

Question

Mathematics

I always thought that a complex function is a composition of several "simple" ones, but is the function g (x) = 5, also a function?
And then if we take the derivative of such a function - f(g(x)), then it turns out to be equal to f'(g(x)) * g'(x)?
And since g'(x) is a constant, then the desired derivative = 0? (because g'(x) = 0)
There may be confusion in the definition of a complex function, but I do not understand how to explain it, for example, to a teacher who may ask in such a formulation.

Answer 1

Yes, the derivative of your complex function f(g(x)) is zero. Simply because your "complex" function actually degenerates into a constant f(5)

Answer 2

If g(x) = 5(constant), then f(g(x)) = f(5) is also a constant, as long as f(x) is a function of one argument. Obviously, the derivative f(g(x))' = 0 in this case.