Let A = {1, 2, 3, 4, 5}, B = N and f: A → B be defined by f(x) = x2.

1.	Let A = {1, 2, 3, 4, 5}, B = N and f: A → B be defined by f(x) = x2. Find the range of f. Identify the type of function.
Answer» A = {1, 2, 3, 4, 5} B = {1, 2, 3, 4 …} f: A → B, f(x) = x² ∴ f(1) = 1² = 1 f(2) = 2² = 4 f(3) = 3² = 9 f(4) = 4² = 16 f(5) = 5² = 25 ∴ Range of f = {1, 4, 9, 16, 25) Elements in A have been different elements in B. Therefore it is one-one function. But not all the elements in B have preimages in A. Therefore it is not on-to function.

Let A = {1, 2, 3, 4, 5}, B = N and f: A → B be defined by f(x) = x2. Find the range of f. Identify the type of function.

Answer»

A = {1, 2, 3, 4, 5}

B = {1, 2, 3, 4 …}

f: A → B, f(x) = x²

∴ f(1) = 1² = 1

f(2) = 2² = 4

f(3) = 3² = 9

f(4) = 4² = 16

f(5) = 5² = 25

∴ Range of f = {1, 4, 9, 16, 25)

Elements in A have been different elements in B.

Therefore it is one-one function. But not all the elements in B have preimages in A. Therefore it is not on-to function.