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The domain and range of the function f: R → R defined by: f = {(x+1, x+5): x ∈ {0, 1, 2, 3, 4, 5}}
- a)Domain = {2, 3, 4, 5, 6}; Range = {6, 7, 8, 9, 10}
- b)Domain = R ; Range = R
- c)Domain = {1, 2, 3, 4, 5, 6}; Range = {5, 6, 7, 8, 9, 10}
- d)Domain = {1, 2, 3, 4, 5}; Range = {5, 6, 7, 8, 9}
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The domain and range of the function f: R → R defined by: f = {(x...
Correct answer is C.
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The domain and range of the function f: R → R defined by: f = {(x...
Domain and Range of the Function:
The domain of a function is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values).
Given function f: R → R, defined by f = {(x, 1, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}, we need to determine the domain and range of this function.
Let's break down the function and find the corresponding values for each x ∈ {0, 1, 2, 3, 4, 5}:
- When x = 0: f(0) = 0 + 5 = 5
- When x = 1: f(1) = 1 + 5 = 6
- When x = 2: f(2) = 2 + 5 = 7
- When x = 3: f(3) = 3 + 5 = 8
- When x = 4: f(4) = 4 + 5 = 9
- When x = 5: f(5) = 5 + 5 = 10
Domain:
The given function is defined for all real numbers (R), as there are no restrictions or limitations mentioned. Therefore, the domain of the function is R.
Range:
From the values obtained for f(x), we can see that the range consists of the set of all possible output values, which are {5, 6, 7, 8, 9, 10}.
Answer Explanation:
Based on the analysis above, we can conclude that the correct option is C:
- Domain = {1, 2, 3, 4, 5, 6}
- Range = {5, 6, 7, 8, 9, 10}
It is important to carefully analyze the given function and determine the domain and range based on the given conditions. In this case, since there are no restrictions mentioned, the domain is R (all real numbers), and the range is the set of output values obtained by substituting the given input values into the function.
The domain of a function is the set of all possible input values (x-values), while the range is the set of all possible output values (y-values).
Given function f: R → R, defined by f = {(x, 1, x + 5): x ∈ {0, 1, 2, 3, 4, 5}}, we need to determine the domain and range of this function.
Let's break down the function and find the corresponding values for each x ∈ {0, 1, 2, 3, 4, 5}:
- When x = 0: f(0) = 0 + 5 = 5
- When x = 1: f(1) = 1 + 5 = 6
- When x = 2: f(2) = 2 + 5 = 7
- When x = 3: f(3) = 3 + 5 = 8
- When x = 4: f(4) = 4 + 5 = 9
- When x = 5: f(5) = 5 + 5 = 10
Domain:
The given function is defined for all real numbers (R), as there are no restrictions or limitations mentioned. Therefore, the domain of the function is R.
Range:
From the values obtained for f(x), we can see that the range consists of the set of all possible output values, which are {5, 6, 7, 8, 9, 10}.
Answer Explanation:
Based on the analysis above, we can conclude that the correct option is C:
- Domain = {1, 2, 3, 4, 5, 6}
- Range = {5, 6, 7, 8, 9, 10}
It is important to carefully analyze the given function and determine the domain and range based on the given conditions. In this case, since there are no restrictions mentioned, the domain is R (all real numbers), and the range is the set of output values obtained by substituting the given input values into the function.
Community Answer
The domain and range of the function f: R → R defined by: f = {(x...
Correct answer is C.
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The domain and range of the function f: R → R defined by: f = {(x+1, x+5): x ∈ {0, 1, 2, 3, 4, 5}}a)Domain = {2, 3, 4, 5, 6}; Range = {6, 7, 8, 9, 10}b)Domain = R ; Range = Rc)Domain = {1, 2, 3, 4, 5, 6}; Range = {5, 6, 7, 8, 9, 10}d)Domain = {1, 2, 3, 4, 5}; Range = {5, 6, 7, 8, 9}Correct answer is option 'C'. Can you explain this answer?
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The domain and range of the function f: R → R defined by: f = {(x+1, x+5): x ∈ {0, 1, 2, 3, 4, 5}}a)Domain = {2, 3, 4, 5, 6}; Range = {6, 7, 8, 9, 10}b)Domain = R ; Range = Rc)Domain = {1, 2, 3, 4, 5, 6}; Range = {5, 6, 7, 8, 9, 10}d)Domain = {1, 2, 3, 4, 5}; Range = {5, 6, 7, 8, 9}Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The domain and range of the function f: R → R defined by: f = {(x+1, x+5): x ∈ {0, 1, 2, 3, 4, 5}}a)Domain = {2, 3, 4, 5, 6}; Range = {6, 7, 8, 9, 10}b)Domain = R ; Range = Rc)Domain = {1, 2, 3, 4, 5, 6}; Range = {5, 6, 7, 8, 9, 10}d)Domain = {1, 2, 3, 4, 5}; Range = {5, 6, 7, 8, 9}Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The domain and range of the function f: R → R defined by: f = {(x+1, x+5): x ∈ {0, 1, 2, 3, 4, 5}}a)Domain = {2, 3, 4, 5, 6}; Range = {6, 7, 8, 9, 10}b)Domain = R ; Range = Rc)Domain = {1, 2, 3, 4, 5, 6}; Range = {5, 6, 7, 8, 9, 10}d)Domain = {1, 2, 3, 4, 5}; Range = {5, 6, 7, 8, 9}Correct answer is option 'C'. Can you explain this answer?.
The domain and range of the function f: R → R defined by: f = {(x+1, x+5): x ∈ {0, 1, 2, 3, 4, 5}}a)Domain = {2, 3, 4, 5, 6}; Range = {6, 7, 8, 9, 10}b)Domain = R ; Range = Rc)Domain = {1, 2, 3, 4, 5, 6}; Range = {5, 6, 7, 8, 9, 10}d)Domain = {1, 2, 3, 4, 5}; Range = {5, 6, 7, 8, 9}Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The domain and range of the function f: R → R defined by: f = {(x+1, x+5): x ∈ {0, 1, 2, 3, 4, 5}}a)Domain = {2, 3, 4, 5, 6}; Range = {6, 7, 8, 9, 10}b)Domain = R ; Range = Rc)Domain = {1, 2, 3, 4, 5, 6}; Range = {5, 6, 7, 8, 9, 10}d)Domain = {1, 2, 3, 4, 5}; Range = {5, 6, 7, 8, 9}Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The domain and range of the function f: R → R defined by: f = {(x+1, x+5): x ∈ {0, 1, 2, 3, 4, 5}}a)Domain = {2, 3, 4, 5, 6}; Range = {6, 7, 8, 9, 10}b)Domain = R ; Range = Rc)Domain = {1, 2, 3, 4, 5, 6}; Range = {5, 6, 7, 8, 9, 10}d)Domain = {1, 2, 3, 4, 5}; Range = {5, 6, 7, 8, 9}Correct answer is option 'C'. Can you explain this answer?.
Solutions for The domain and range of the function f: R → R defined by: f = {(x+1, x+5): x ∈ {0, 1, 2, 3, 4, 5}}a)Domain = {2, 3, 4, 5, 6}; Range = {6, 7, 8, 9, 10}b)Domain = R ; Range = Rc)Domain = {1, 2, 3, 4, 5, 6}; Range = {5, 6, 7, 8, 9, 10}d)Domain = {1, 2, 3, 4, 5}; Range = {5, 6, 7, 8, 9}Correct 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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