Functions-8

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Express the following functions as sets of ordered pairs and determine their ranges
(a) f : A → R, f(x) = x2 + 1, where A = {-1, 0, 2, 4}
(b) g : A → N, g(x) = 2x, where A = {x : x ∈ N, x ≤ 10}.

Solution: (a) We have, f(-1) = (-1)2 + 1 = 2,

f(0) = 02 + 1 = 1, f(2) = 22 + 1 = 5 and f(4) = 42 + 1 = 17

So, f = {(x, f(x)) : x ∈ A} = {(-1, 2), (0,1), (2,5), (4,17)}

So, Range of (f) = {2, 15, 17}

(b) We have, A = {1, 2, 3, …, 10}. So,

g(1) = 2 X 1= 2, g(2) = 2 X 2 = 4, g(3) = 2 X 3 = 6, g(4) = 2 X 4 = 8, g(5) = 2 X 5 = 10, g(6) = 2 X 6 = 12, g(7) = 2 X 7 = 14, g(8) =

2 X 8 = 16, g(9) = 2 X 9 = 18 and g(10) = 2 X 10 = 20.

Therefore, g = {(x, g(x) : x ∈ A)} = {(1, 2), (2, 4), (3, 6), …..,(10, 20)}

Range of g = g(A) = {g(x) : x ∈ A} = {2, 4, 6, 8,10, 12,14, 16, 18, 20}

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