Given f: R → R is a function defined by
Injectivity:
Let x and y be any two elements in the domain (R), such that f(x) = f(y)
⇒
⇒
⇒
⇒ x = y
So, f is one-one.
Surjectivity:
Let y be any element in the co-domain (R), such that f(x) = y for some element x in R (domain)
f(x) = y
⇒
⇒
⇒
⇒
in R
So, for every element in the co-domain, there exists some pre-image in the domain. f is onto.
Since, f is both one-to-one and onto, it is a bijection.