If A = {1, 2, 3, 4}, B = (1, 2, 3, 4, 5, 6} are two sets, and the function f: A → B is defined by f(x) = x + 2; for all x ∈A, then the function f is onto.Group startsTrue or FalseTrue, unselectedFalse, unselected
Question
If A = {1, 2, 3, 4}, B = (1, 2, 3, 4, 5, 6} are two sets, and the function f: A → B is defined by f(x) = x + 2; for all x ∈A, then the function f is onto.Group startsTrue or FalseTrue, unselectedFalse, unselected
Solution
To determine if the function f: A → B is onto, we need to check if every element in set B has a corresponding element in set A such that f(x) = x + 2.
Step 1: Identify the elements in set B. B = (1, 2, 3, 4, 5, 6}
Step 2: Apply the function f(x) = x + 2 to each element in set A. f(1) = 1 + 2 = 3 f(2) = 2 + 2 = 4 f(3) = 3 + 2 = 5 f(4) = 4 + 2 = 6
Step 3: Check if every element in set B has a corresponding element in set A after applying the function. In this case, every element in set B (1, 2, 3, 4, 5, 6) has a corresponding element in set A (1, 2, 3, 4) after applying the function f(x) = x + 2.
Therefore, the function f is onto.
Answer: True.
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