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Let f be a function defined so that every element of the codomain has at most two pre-images and there is at least one element in the co-domain which has exactly two pre-images we shall call this function as “two-one” function. A two-one function is definitely a many one function but vice-versa is not true. For example, y = |ex – 1| is a “two-one” function. y = x3 – x is a many one function but not a “two-one” function. In the light of above definition answer the following questions:
Q. In the following functions which one is a “two-one” function :-
  • a)
    y = |ln|x||
  • b)
    y = x2 sin x    
  • c)
    y = x3 + 3x + 1
  • d)
    y = x4 – x + 1
Correct answer is option 'D'. Can you explain this answer?
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Let f be a function defined so that every element of the codomain has at most two pre-images and there is at least one element in the codomain which has exactly two pre-images. We shall call this function as "two-to-one".

In a "two-to-one" function, each element in the codomain can have at most two pre-images. This means that for every y in the codomain, there can be at most two x values in the domain such that f(x) = y.

Additionally, there must exist at least one element in the codomain which has exactly two pre-images. This means that there is at least one y in the codomain such that there are two distinct x values, say x1 and x2, in the domain such that f(x1) = y and f(x2) = y.

Overall, a "two-to-one" function is a function that is not one-to-one (since there can be at most two pre-images for each element in the codomain), but each element in the codomain has at most two pre-images.
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Let f be a function defined so that every element of the codomain has at most two pre-images and there is at least one element in the co-domain which has exactly two pre-images we shall call this function as “two-one” function. A two-one function is definitely a many one function but vice-versa is not true. For example, y = |ex – 1| is a “two-one” function. y = x3 – x is a many one function but not a “two-one” function. In the light of above definition answer the following questions:Q.In the following functions which one is a “two-one” function :-a)y = |ln|x||b)y = x2 sin x c)y = x3 + 3x + 1d)y = x4 – x + 1Correct answer is option 'D'. Can you explain this answer?
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Let f be a function defined so that every element of the codomain has at most two pre-images and there is at least one element in the co-domain which has exactly two pre-images we shall call this function as “two-one” function. A two-one function is definitely a many one function but vice-versa is not true. For example, y = |ex – 1| is a “two-one” function. y = x3 – x is a many one function but not a “two-one” function. In the light of above definition answer the following questions:Q.In the following functions which one is a “two-one” function :-a)y = |ln|x||b)y = x2 sin x c)y = x3 + 3x + 1d)y = x4 – x + 1Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Let f be a function defined so that every element of the codomain has at most two pre-images and there is at least one element in the co-domain which has exactly two pre-images we shall call this function as “two-one” function. A two-one function is definitely a many one function but vice-versa is not true. For example, y = |ex – 1| is a “two-one” function. y = x3 – x is a many one function but not a “two-one” function. In the light of above definition answer the following questions:Q.In the following functions which one is a “two-one” function :-a)y = |ln|x||b)y = x2 sin x c)y = x3 + 3x + 1d)y = x4 – x + 1Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f be a function defined so that every element of the codomain has at most two pre-images and there is at least one element in the co-domain which has exactly two pre-images we shall call this function as “two-one” function. A two-one function is definitely a many one function but vice-versa is not true. For example, y = |ex – 1| is a “two-one” function. y = x3 – x is a many one function but not a “two-one” function. In the light of above definition answer the following questions:Q.In the following functions which one is a “two-one” function :-a)y = |ln|x||b)y = x2 sin x c)y = x3 + 3x + 1d)y = x4 – x + 1Correct answer is option 'D'. Can you explain this answer?.
Solutions for Let f be a function defined so that every element of the codomain has at most two pre-images and there is at least one element in the co-domain which has exactly two pre-images we shall call this function as “two-one” function. A two-one function is definitely a many one function but vice-versa is not true. For example, y = |ex – 1| is a “two-one” function. y = x3 – x is a many one function but not a “two-one” function. In the light of above definition answer the following questions:Q.In the following functions which one is a “two-one” function :-a)y = |ln|x||b)y = x2 sin x c)y = x3 + 3x + 1d)y = x4 – x + 1Correct answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE. Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Let f be a function defined so that every element of the codomain has at most two pre-images and there is at least one element in the co-domain which has exactly two pre-images we shall call this function as “two-one” function. A two-one function is definitely a many one function but vice-versa is not true. For example, y = |ex – 1| is a “two-one” function. y = x3 – x is a many one function but not a “two-one” function. In the light of above definition answer the following questions:Q.In the following functions which one is a “two-one” function :-a)y = |ln|x||b)y = x2 sin x c)y = x3 + 3x + 1d)y = x4 – x + 1Correct answer is option 'D'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Let f be a function defined so that every element of the codomain has at most two pre-images and there is at least one element in the co-domain which has exactly two pre-images we shall call this function as “two-one” function. A two-one function is definitely a many one function but vice-versa is not true. For example, y = |ex – 1| is a “two-one” function. y = x3 – x is a many one function but not a “two-one” function. In the light of above definition answer the following questions:Q.In the following functions which one is a “two-one” function :-a)y = |ln|x||b)y = x2 sin x c)y = x3 + 3x + 1d)y = x4 – x + 1Correct answer is option 'D'. Can you explain this answer?, a detailed solution for Let f be a function defined so that every element of the codomain has at most two pre-images and there is at least one element in the co-domain which has exactly two pre-images we shall call this function as “two-one” function. A two-one function is definitely a many one function but vice-versa is not true. For example, y = |ex – 1| is a “two-one” function. y = x3 – x is a many one function but not a “two-one” function. In the light of above definition answer the following questions:Q.In the following functions which one is a “two-one” function :-a)y = |ln|x||b)y = x2 sin x c)y = x3 + 3x + 1d)y = x4 – x + 1Correct answer is option 'D'. Can you explain this answer? has been provided alongside types of Let f be a function defined so that every element of the codomain has at most two pre-images and there is at least one element in the co-domain which has exactly two pre-images we shall call this function as “two-one” function. A two-one function is definitely a many one function but vice-versa is not true. For example, y = |ex – 1| is a “two-one” function. y = x3 – x is a many one function but not a “two-one” function. In the light of above definition answer the following questions:Q.In the following functions which one is a “two-one” function :-a)y = |ln|x||b)y = x2 sin x c)y = x3 + 3x + 1d)y = x4 – x + 1Correct answer is option 'D'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Let f be a function defined so that every element of the codomain has at most two pre-images and there is at least one element in the co-domain which has exactly two pre-images we shall call this function as “two-one” function. A two-one function is definitely a many one function but vice-versa is not true. For example, y = |ex – 1| is a “two-one” function. y = x3 – x is a many one function but not a “two-one” function. In the light of above definition answer the following questions:Q.In the following functions which one is a “two-one” function :-a)y = |ln|x||b)y = x2 sin x c)y = x3 + 3x + 1d)y = x4 – x + 1Correct answer is option 'D'. Can you explain this answer? tests, examples and also practice JEE tests.
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