This is a question of my last exam in Functional Analysis of my graduation:
Consider that norm: $|f|=\int_0^1 x^2 f(x)$ where $f\in C^0([0,1])$. Show that the linear operator $f(1-x)\in C^0([0,1])$ is not continuous.
I show that this operator is bounded with norm 1. So the operator is continuous and the teacher give me 0 in this question
MY FRIENDS ATTEMPT
Talking with my friends, they say that: "This norm is more "refined" that the L1 norm, so the operator is limited."
MY TEACHER BLA BLA BLA He say the operator is NOT limited but don't say the demonstration
I believe that all is wrong but I don't know how to show this...