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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. The values of ‘a’ for which the function f(x) = x4 – ax2 is a “two-one” function are
- a)a < 1
- b)a > 0
- c)a < 0
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Identifying the Function:
To determine the values of 'a' for which the function f(x) = x^4 - ax^2 is a "two-one" function, we need to understand the characteristics of a "two-one" function.
Characteristics of a "Two-One" Function:
- Every element in the codomain has at most two pre-images.
- At least one element in the codomain has exactly two pre-images.
Analysis of the Given Function:
In the function f(x) = x^4 - ax^2, the power of x is always even. This means that the function is symmetric about the y-axis.
To ensure that the function is a "two-one" function, we need to have at least one element in the codomain with exactly two pre-images. This happens when the function is not one-to-one, i.e., when multiple inputs map to the same output.
Determining the Values of 'a':
For the function f(x) = x^4 - ax^2 to be a "two-one" function, the leading coefficient of the function (coefficient of x^4) should be positive. This ensures that the function opens upwards, allowing for multiple inputs to map to the same output.
If we set a < 0,="" the="" leading="" coefficient="" becomes="" negative,="" and="" the="" function="" would="" open="" downwards,="" making="" it="" a="" many-one="" function="" but="" not="" a="" "two-one"="" />
Therefore, the correct answer is option 'C' (a < 0),="" as="" it="" ensures="" the="" function="" f(x)="x^4" -="" ax^2="" is="" a="" "two-one"="" function.="" 0),="" as="" it="" ensures="" the="" function="" f(x)="x^4" -="" ax^2="" is="" a="" "two-one"="" />
To determine the values of 'a' for which the function f(x) = x^4 - ax^2 is a "two-one" function, we need to understand the characteristics of a "two-one" function.
Characteristics of a "Two-One" Function:
- Every element in the codomain has at most two pre-images.
- At least one element in the codomain has exactly two pre-images.
Analysis of the Given Function:
In the function f(x) = x^4 - ax^2, the power of x is always even. This means that the function is symmetric about the y-axis.
To ensure that the function is a "two-one" function, we need to have at least one element in the codomain with exactly two pre-images. This happens when the function is not one-to-one, i.e., when multiple inputs map to the same output.
Determining the Values of 'a':
For the function f(x) = x^4 - ax^2 to be a "two-one" function, the leading coefficient of the function (coefficient of x^4) should be positive. This ensures that the function opens upwards, allowing for multiple inputs to map to the same output.
If we set a < 0,="" the="" leading="" coefficient="" becomes="" negative,="" and="" the="" function="" would="" open="" downwards,="" making="" it="" a="" many-one="" function="" but="" not="" a="" "two-one"="" />
Therefore, the correct answer is option 'C' (a < 0),="" as="" it="" ensures="" the="" function="" f(x)="x^4" -="" ax^2="" is="" a="" "two-one"="" function.="" 0),="" as="" it="" ensures="" the="" function="" f(x)="x^4" -="" ax^2="" is="" a="" "two-one"="" />
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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.The values of ‘a’ for which the function f(x) = x4 – ax2 is a “two-one” function area)a < 1b)a > 0c)a < 0d)None of theseCorrect answer is option 'C'. 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.The values of ‘a’ for which the function f(x) = x4 – ax2 is a “two-one” function area)a < 1b)a > 0c)a < 0d)None of theseCorrect answer is option 'C'. 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.The values of ‘a’ for which the function f(x) = x4 – ax2 is a “two-one” function area)a < 1b)a > 0c)a < 0d)None of theseCorrect answer is option 'C'. 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.The values of ‘a’ for which the function f(x) = x4 – ax2 is a “two-one” function area)a < 1b)a > 0c)a < 0d)None of theseCorrect answer is option 'C'. Can you explain this answer?.
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.The values of ‘a’ for which the function f(x) = x4 – ax2 is a “two-one” function area)a < 1b)a > 0c)a < 0d)None of theseCorrect answer is option 'C'. 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.The values of ‘a’ for which the function f(x) = x4 – ax2 is a “two-one” function area)a < 1b)a > 0c)a < 0d)None of theseCorrect answer is option 'C'. 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.The values of ‘a’ for which the function f(x) = x4 – ax2 is a “two-one” function area)a < 1b)a > 0c)a < 0d)None of theseCorrect answer is option 'C'. 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.The values of ‘a’ for which the function f(x) = x4 – ax2 is a “two-one” function area)a < 1b)a > 0c)a < 0d)None of theseCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
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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.The values of ‘a’ for which the function f(x) = x4 – ax2 is a “two-one” function area)a < 1b)a > 0c)a < 0d)None of theseCorrect answer is option 'C'. 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.The values of ‘a’ for which the function f(x) = x4 – ax2 is a “two-one” function area)a < 1b)a > 0c)a < 0d)None of theseCorrect answer is option 'C'. 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.The values of ‘a’ for which the function f(x) = x4 – ax2 is a “two-one” function area)a < 1b)a > 0c)a < 0d)None of theseCorrect answer is option 'C'. 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.The values of ‘a’ for which the function f(x) = x4 – ax2 is a “two-one” function area)a < 1b)a > 0c)a < 0d)None of theseCorrect answer is option 'C'. 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.The values of ‘a’ for which the function f(x) = x4 – ax2 is a “two-one” function area)a < 1b)a > 0c)a < 0d)None of theseCorrect answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
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