Define the into function. Give an example.

1.	Define the into function. Give an example.
Answer» Into Function A function f: A → B is said to be into if there exists even a single element in B having no pre-image in A. So, f is into range (f) ⊂ B. Example: Let A = {2, 3, 5, 7} and B = {0, 1, 3, 5, 7} Let f: A → B: f(x) = (x – 2) then f(2) = (2 – 2) = 0 f(3) = (3 – 2) = 1 f(5) = (5 – 2) = 3 f(7) = (7 – 2) = 5 Thus, every element in A has a unique image in B Now ∃ 7 ∈ B having no pre-image in A Hence, f is into.

Answer»

Into Function

A function f: A → B is said to be into if there exists even a single element in B having no pre-image in A.

So, f is into range (f) ⊂ B.

Example:

Let A = {2, 3, 5, 7} and B = {0, 1, 3, 5, 7}

Let f: A → B: f(x) = (x – 2) then

f(2) = (2 – 2) = 0

f(3) = (3 – 2) = 1

f(5) = (5 – 2) = 3

f(7) = (7 – 2) = 5

Thus, every element in A has a unique image in B

Now ∃ 7 ∈ B having no pre-image in A

Hence, f is into.

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