from finding the inverse function, evaluating function and operation with functions,

Question

Does the order of composition matters?

 

Answer 1

Short answer: Yes it does.

 

Here is an example.

 

f(x) = 3x

g(x) = x²

 

(f°g)(x)=f(x²)=3*(x²)=3x²

(g°f)(x)=g(3x)=(3x)²=9x²

 

I haven't proven this vigorously, but I conjecture that there are more examples where the order matters than when it doesn't.