Ok. Today I would like to continue my last blog post. It’s about a composite function. It follows a rule:f(g(x))≠g(f(x))≠f(x).g(x). In nature, there are a lot of phenomenons which don’t follow science. There are also many special conditions which don’t follow math rules. In this example, there is a very special condition which can make f(g(x)), g(f(x)) and f(x).g(x) be equal. When f(x)=g(x)=x², f(g(x))=(x²)²=x⁴, g(f(x))=(x²)²=x⁴ and f(x).g(x)=x².x²=x⁴. Therefore, f(g(x))=g(f(x))=f(x).g(x)=x⁴ when f(x)=g(x)=x².
In most of the situations in this math rule, it is not possible for these three terms to be equal. But when f(x)=g(x)=x², you can find so amazing thing happening. Math is so magical!!! There are a lot of math fields still needed to be research, and I believe everyone can be a mathematician if they are interested in math.