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## Main Question or Discussion Point

I want to let f and g be functions to be defined on a common domain D. Then the maximum and minimum functions are defined as follows for any x belonging to D....

max(f,g)(x) = f(x), if f(x) >= g(x)

max(f,g)(x) = g(x), if g(x) > f(x)

and

min(f, g)(x) = f(x), if f(x) <= g(x)

min(f, g)(x) = g(x), if g(x) < f(x)

How do I define my max(sinx, cosx) and min(x, x^2)?

max(f,g)(x) = f(x), if f(x) >= g(x)

max(f,g)(x) = g(x), if g(x) > f(x)

and

min(f, g)(x) = f(x), if f(x) <= g(x)

min(f, g)(x) = g(x), if g(x) < f(x)

How do I define my max(sinx, cosx) and min(x, x^2)?