Determine whether each of these functions is a bijection from r to r.

a. f (x) = 2x + 1

b. f (x) = x2 + 1

Determine the type of each function from R to R a) f (x) = 2x + 1 Bijective This is injective because for every a 6 = b, we have f (a) 6 = f (b) (every number is 1 more than 2 times some number). We also know that the function is surjective because the range is all real numbers from 2 ((yâ’1) / 2) + 1 = y. b) f (x) = x2 + 1 Not injective and not surjective. We know the function is not injective because we can have the same value for f (x) given two different x values. For example, f (2) = 22 + 1 = 5 and f (â’2) = (â’2) 2 + 1 = 5. The function is also not surjective because the range is all real numbers greater than or equal to 1, or can be written as [1,âž).