CA Foundation Exam > CA Foundation Questions > The function f(x) = 2x isa)one-one mappingb)o...
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The function f(x) = 2x is
- a)one-one mapping
- b)one-many
- c)many-one
- d)none of these
Correct answer is option 'A'. Can you explain this answer?
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The function f(x) = 2x isa)one-one mappingb)one-manyc)many-oned)none o...
Solution:Given function f(x) = 2xTo determine whether the given function is one-one or many-one, we need to check whether each element of the domain is mapped to a unique element in the range or not. One-one Mapping:A function is said to be one-one or injective if each element of the domain is mapped to a unique element in the range. Let's check whether the given function is one-one or not.Assume that f(x1) = f(x2) for some x1, x2 ∈ R.Then, 2x1 = 2x2Dividing both sides by 2, we getx1 = x2Hence, we can conclude that for any two distinct elements x1, x2 in the domain, f(x1) ≠ f(x2). Therefore, the given function is a one-one mapping.Option (a) is correct.Many-one Mapping:A function is said to be many-one or non-injective if there exist at least one element in the domain which is mapped to two or more elements in the range. Since the given function is one-one, it cannot be many-one.Option (b) is incorrect.Option (c) is also incorrect.None of these:Since option (a) is correct, option (d) is incorrect.Therefore, the correct option is (a) one-one mapping.
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The function f(x) = 2x isa)one-one mappingb)one-manyc)many-oned)none of theseCorrect answer is option 'A'. Can you explain this answer?
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