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The function, f(x) = 2x - 1 is
- a)It is not surjective
- b)It is surjective
- c)It is surjective in some intervals of the domain
- d)Insufficient information
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The function, f(x) = 2x - 1 isa)It is not surjectiveb)It is surjective...
The function f(x) = 2x - 1 is surjective.
Explanation:
A function is surjective (also called onto) if for every element y in the codomain, there exists an element x in the domain such that f(x) = y.
In this case, the function f(x) = 2x - 1 is a linear function. For any given y value, we can find an x value such that f(x) = y:
y = 2x - 1
x = (y + 1) / 2
So, for any y value, there exists an x value that satisfies the equation. Therefore, the function is surjective.
Explanation:
A function is surjective (also called onto) if for every element y in the codomain, there exists an element x in the domain such that f(x) = y.
In this case, the function f(x) = 2x - 1 is a linear function. For any given y value, we can find an x value such that f(x) = y:
y = 2x - 1
x = (y + 1) / 2
So, for any y value, there exists an x value that satisfies the equation. Therefore, the function is surjective.
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Community Answer
The function, f(x) = 2x - 1 isa)It is not surjectiveb)It is surjective...
Explanation:
Analysis of the given function:
Conclusion:
A function is said to be surjective if every element of the co-domain has a pre-image in the domain. In other words, every element of the co-domain is mapped to by at least one element of the domain.
Analysis of the given function:
The given function is f(x) = 2x + 1. Let Y be the co-domain of the function.
- The domain of the function is R (set of all real numbers).
- The co-domain of the function is also R.
- For any y in the co-domain, we can find an x in the domain such that f(x) = y. This is because we can solve the equation y = 2x + 1 for x, which gives x = (y - 1)/2. Therefore, every element of the co-domain has a pre-image in the domain.
Conclusion:
Since every element of the co-domain has a pre-image in the domain, the given function is surjective. Therefore, the correct answer is option B.
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The function, f(x) = 2x - 1 isa)It is not surjectiveb)It is surjectivec)It is surjective in some intervals of the domaind)Insufficient informationCorrect answer is option 'B'. Can you explain this answer?
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