How to show $\phi $ is an injective map?

Question

I'm trying to show that $\phi$ is an injective map for this i'm trying to show $\phi(t_1)=\phi(t_2)\implies t_1=t_2$

let $$\phi(t_1)=\phi(t_2)$$ $$\implies \varphi_{t_1}=\varphi_{t_2}$$ $$\implies \varphi_{t_1}(f)=\varphi_{t_2}(f)\forall f\in C^n[a,b]$$ $$\implies f({t_1})=f({t_2})$$ from here i'm not getting how to show $t_1=t_2$?

Source:A Course in Commutative Banach Algebras by Eberhard Kaniuth