I need to show that the operator $\displaystyle T:L^2([0,1],\mathbb{R}) \rightarrow L^2([0,1],\mathbb{R})$ defined by $\displaystyle (Tf)(x)=xf(x)$ has norm 1

There is a hint on the question saying show it must be at least $\displaystyle 1-\frac{1}{n}$ for all $\displaystyle n$

The norm for $\displaystyle L^2$ is $\displaystyle \|f\|_2=\left(\int_{0}^{1}|f(x)|^2dx\right)^\frac{ 1}{2}$

Any help would be great

Thanks