Functions-1

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Given A = { -1, 0, 2, 5, 6, 11}, B = {-2, -1, 0, 18, 28, 108} and f(x) = x² - x – 2. Is f(A) = B? Find f(A).

Solution: We have :

f(-1) = (-1)² - (-1) – 2 = 0, f(0) =0² - 0 – 2 = -2,

f(2) = 2² - 2 – 2 = 0, f(5) = 5² - 5 – 2 = 18,

f(6) = 6² - 6 – 2 = 28 and f(11) = 11² - 11 – 2 = 108.

Therefore, f(A) = {f(x) : x ∈ A} = {f(-1), f(0), f(2), f(5), f(6), f(11)} = {0, -2, 18, 28, 108}

We observe that -1 ∈ B but -1 ∉ f(A). So, f(A) ≠ B.