What's the adjoint of a translation operator on a Hilbert space?

Question

Let $H$ be a $\mathbb R$-Hilbert space, $x\in H$ and $$\tau_x:H\to H\;,\;\;\;y\mapsto y+x.$$

What's the adjoint operator of $\tau_x$?

This should be an easy question, but I'm not able to deduce the answer. $\tau_x$ is clearly not self-adjoint, when $x\ne0$, since $$\forall y,z\in H:\langle\tau_xy,z\rangle-\langle y,\tau_xz\rangle=\langle x,y-z\rangle\tag1.$$

Answer 1

Your question does not make sense. Adjoint is defined only for linear operators, and when $x \ne 0$ your map is not linear.