Is a one-to-one correspondence a function? Explain your answer and given an example.
Choose the correct answer below.
A. Yes, by definition a function from set A to set B is a correspondence in which each element of A is paired with one, and only one, element of B, and this is a one-to-one correspondence. An example is $y = x^2$.
B. No, by definition a function is a correspondence between two sets, A and B, such that each element from A is paired with exactly one element of B, but this is not true of a one-to-one correspondence. An example is $y = x^2$.
C. No, a one-to-one correspondence is not a function because there is only one possible value y for each value x. An example is $y = \sqrt{x}$.
D. Yes, a one-to-one correspondence implies that for each input there is one, and only one, output. An example is $x = y^2$.
