If f: A → M, A = {x | x ∈ N, 1 ≤ x < 5} and M = {x

1.	If f: A → M, A = {x \| x ∈ N, 1 ≤ x < 5} and M = {x \| x ∈ N, 1 ≤ x ≤ 20} and f(x) = x2 + 1, then find the range of f.
Answer» f: A → M A = {x \| x ∈ N, 1 ≤ x < 5} = {1, 2, 3, 4} M = {x \| x G N, 1 ≤ x ≤ 20} = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20} f(x) = x² + 1 Range of f R_f= {f(x) \| x ∈ A} = {f(1), f(2), f(3), f(4)} Now, f(x) = x² + 1 ∴ f(1) = (1)² + 1 = 1 + 1 = 2 f(2) = (2)² + 1 = 4+ 1 = 5 f(3) = (3)² + 1 = 9 + 1 = 10 f(4) = (4)² + 1 = 16 + 1 = 17 Hence, Range of f R_f = {2, 5, 10, 17}

If f: A → M, A = {x | x ∈ N, 1 ≤ x < 5} and M = {x | x ∈ N, 1 ≤ x ≤ 20} and f(x) = x2 + 1, then find the range of f.

Answer»

f: A → M

A = {x | x ∈ N, 1 ≤ x < 5}

= {1, 2, 3, 4}

M = {x | x G N, 1 ≤ x ≤ 20}

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}

f(x) = x² + 1

Range of f R_f= {f(x) | x ∈ A}

= {f(1), f(2), f(3), f(4)}

Now, f(x) = x² + 1

∴ f(1) = (1)² + 1 = 1 + 1 = 2

f(2) = (2)² + 1 = 4+ 1 = 5

f(3) = (3)² + 1 = 9 + 1 = 10

f(4) = (4)² + 1 = 16 + 1 = 17

Hence, Range of f R_f = {2, 5, 10, 17}