The function f: R → R, f(x) = 2x + 1 is bijective, since for each y there is a unique x = (y − 1)/2 such that f(x) = y. More generally, any linear function over the reals, f: R → R, f(x) = ax + b (where a is non-zero) is a bijection.
What is bijective function with example?
Alternatively, f is bijective if it is a one-to-one correspondence between those sets, in other words both injective and surjective. Example: The function f(x) = x2 from the set of positive real numbers to positive real numbers is both injective and surjective. Thus it is also bijective.
Which function is not bijective function?
Example 1: The function f (x) = x2 from the set of positive real numbers to positive real numbers is injective as well as surjective. Thus, it is also bijective. However, the same function from the set of all real numbers R is not bijective since we also have the possibilities f (2)=4 and f (-2)=4.
