Proving that a relation is an equivalence relation by proving it is transitive

Question

I came up with this question , which I have to prove that it is an equivalence relation

Define a function f : R → R by f(x) = x^2 + 1. For a, b ∈ R define a ≃ b to mean that f(a) = f(b)

I have done proving that it is a reflexive and also symmetric , I am bit stuck at the transitive part Thankyou so much.

Answer 1

If $f(a)=f(b)$ and $f(b)=f(c)$, then $f(a)=f(c)$. This works for every function, not just for that one.