CA Foundation · Quantitative Aptitude · Sets, Relations and Functions, Limits and Continuity
Let A = {1, 2, 3, 4} and B = {2, 4, 6, 8}. A function f : A → B is defined as f(x) = 2x. How many elements are in the range of f?
The function f(x) = 2x maps elements of A as follows: f(1)=2, f(2)=4, f(3)=6, f(4)=8. All four values belong to B, so the range is {2, 4, 6, 8} with 4 elements.
- A2
- B3
- C4Correct
- D1
Explanation
The range of a function is the set of all output values actually attained. Applying f(x) = 2x: f(1) = 2, f(2) = 4, f(3) = 6, f(4) = 8. The range is {2, 4, 6, 8}, which has 4 elements. However, we must check if all these values exist in B. All of {2, 4, 6, 8} are in B, so the range contains 4 elements. Wait—re-reading: all four outputs are achieved and in B. The range has 4 elements. If the question intends the answer to be unique, the correct count is 4, but option (c) states 4.
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