**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.**