Operator norm of $T: L^{p}(0,\infty) \rightarrow L^{p}(0,\infty)$

Question

I hope you can help me with this exercise.

Let $p\in (1,\infty)$. Also,

\begin{align*} T: L^{p}(0,\infty) &\rightarrow L^{p}(0,\infty)\\ f&\rightarrow (Tf)(x)=\frac{1}{x}\int_{0}^{x} f(y)\, dy \end{align*}

(1) Show that $T$ is well defined and is continuous.

(2) $\|T\|=\dfrac{p}{p-1}.$

Thank you in advance!