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The function f (x) = 10x from R to [0,∞] is
- a)one-one and onto
- b)one-one and into
- c)a constant function
- d)an identity function
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The function f (x) = 10x from R to [0,∞] isa)one-one and ontob)one-one...
One-one and Onto Function Explanation:
One-one Function:
- A function is said to be one-one if each element of the domain maps to a unique element in the codomain.
- In this case, for the function f(x) = 10x, for every unique x in the domain, there exists a unique value in the codomain.
- Therefore, the function f(x) = 10x is one-one.
Onto Function:
- A function is said to be onto if every element in the codomain is the image of at least one element in the domain.
- In this case, the function f(x) = 10x maps every real number to a non-negative real number.
- Hence, every element in the codomain [0, ∞] has a pre-image in the domain R.
- Therefore, the function f(x) = 10x is onto.
Conclusion:
- The function f(x) = 10x is both one-one and onto, making it a bijection from the set of real numbers to the interval [0, ∞].
- Since the function is both one-one and onto, it satisfies the conditions of being a bijective function.
One-one Function:
- A function is said to be one-one if each element of the domain maps to a unique element in the codomain.
- In this case, for the function f(x) = 10x, for every unique x in the domain, there exists a unique value in the codomain.
- Therefore, the function f(x) = 10x is one-one.
Onto Function:
- A function is said to be onto if every element in the codomain is the image of at least one element in the domain.
- In this case, the function f(x) = 10x maps every real number to a non-negative real number.
- Hence, every element in the codomain [0, ∞] has a pre-image in the domain R.
- Therefore, the function f(x) = 10x is onto.
Conclusion:
- The function f(x) = 10x is both one-one and onto, making it a bijection from the set of real numbers to the interval [0, ∞].
- Since the function is both one-one and onto, it satisfies the conditions of being a bijective function.
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The function f (x) = 10x from R to [0,∞] isa)one-one and ontob)one-one and intoc)a constant functiond)an identity functionCorrect answer is option 'B'. Can you explain this answer?
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