Answer to Question #345964 in Discrete Mathematics for asasas

Question #345964

Determine whether each of these functions from Z to Z is one-to-one.


a. f(n) = n2


+ 1


b. f(n) = n


1
Expert's answer
2022-05-30T14:56:31-0400

a. Let "n_1=-1, n_2=1, n_1, n_2\\in \\Z,n_1\\not=n_2"


"f(n_1)=f(-1)=(-1)^2+1=2"

"f(n_2)=f(1)=(1)^2+1=2"

We see that

"f(n_1)=f(-1)=1=f(1)=f(n_2),"

but "n_1=-1\\not=1=n_2."

Therefore the function "f(n)=n^2+1, n\\in \\Z" is not one-to-one from "\\Z" to "\\Z."


b. Let "f(n_1)=f(n_2)." It means that

"n_1=n_2"

The function "f(n)=n" is bijective (one-to-one ) from "\\Z" to "\\Z."



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