A function f : A B defined as f(x) = 2x is both one-one and onto. IfA = {1, 2, 3, 4}, then find the set B.
Question
A function f : A B defined as f(x) = 2x is both one-one and onto. IfA = {1, 2, 3, 4}, then find the set B.
Solution
The function f(x) = 2x is defined as taking an element from set A and multiplying it by 2.
Step 1: Identify the elements in set A. Set A = {1, 2, 3, 4}
Step 2: Apply the function to each element in set A. f(1) = 21 = 2 f(2) = 22 = 4 f(3) = 23 = 6 f(4) = 24 = 8
Step 3: The set B is the set of all outputs of the function f when applied to elements in set A. So, set B = {2, 4, 6, 8}
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