Demonstration for one-to-one function

Question

Show that f is a function one-to-one, if and only if f(x) = 0 for x=0.
I cannot solve this demonstration, I know that if both elements are the same and their functions are the same, then is one to one, but in this case they only show me one element. Please help.

Answer 1

"I know that if both elements are the same and their functions are the same, then is one to one" is not correct.

https://study.com/academy/lesson/one-to-one-functions-definitions-and-examples.html