Solution:
Option A:
Given: f (x) = x, ∀ x ∈ A, where A = {1, 2, 3, 4, 5} and f is a function on A.
As we know that the given function is an identity function which is both one-one and onto.
∴ The given function f(x) = x, is not an into function.
Option B:
Given: f (x) = x + 1, ∀ x ∈ A, where f is a function from A = {1, 2, 3, 4, 5} to B = {2, 3, 4, 5, 6, 7}.
⇒ f(1) = 2 ∈ B, f(2) = 3 ∈ B, f(3) = 4 ∈ B, f(4) = 5 ∈ B, f(5) = 6 ∈ B.
So, Codomain of the given function is B = {2, 3, 4, 5, 6, 7} and range of the function f is {2, 3, 4, 5, 6}
⇒ Range of function f ⊂ Co-domain of function f
Hence, the given function is an into function.
Option C:
Given: f (x) = 2x, ∀ x ∈ A, where f is a function from A = {1, 2, 3, 4, 5} to B = {2, 4, 6, 8, 10, 12}
⇒ f(1) = 2 ∈ B, f(2) = 4 ∈ B, f(3) = 6 ∈ B, f(4) = 8 ∈ B, f(5) = 10 ∈ B.
So, Codomain of the given function is B = {2, 4, 6, 8, 10, 12} and range of the function f is {2, 4, 6, 8, 10}
⇒ Range of function f ⊂ Co-domain of function f Hence, the given function is an into function.
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