Why is $\operatorname{supp}(τ_hf) =h + \operatorname{supp}(f)$?
Let $f\colon \mathbb R^n\to\mathbb R$ be a continuous function. Define $τ_hf$ by $(τ_hf)(x)=f(x-h)$ translation of $f$ by $h$.
Prove $\operatorname{supp}(τ_hf) =h + \operatorname{supp}(f)$
I'm trying to understand why this happens.
I am trying to prove by double inclusion. Let $A =\operatorname{supp}(τ_hf)$ and $B = h + \operatorname{supp}(f)$ .
I took an element in $A$ and I can't get that this element is also in $B$. (In similar way if I take an element in $B$ I can't get to $A$.) I don't know if I'm going the right way in this prove.
I would really appreciate if someone could help me with this prove or give me some idea how to do it.
Thanks