CA Foundation Exam > CA Foundation Questions > The domain and range of {(x,y) : Y = x2} isa)...
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The domain and range of {(x,y) : Y = x2} is
- a)(reals, natural numbers)
- b)(reals, positive reals)
- c)(reals, reals)
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The domain and range of {(x,y) : Y = x2} isa)(reals, natural numbers)b...
Explanation:
The given set is {(x,y) : Y = x2}. This represents a parabola in the Cartesian plane. The domain of this set is the set of all real numbers, because for any real value of x, we can find a corresponding value of y (x2) which belongs to the set.
The range of this set is the set of all positive real numbers, because y (x2) is always greater than or equal to zero, and can take on any positive value. Therefore, the range of the set is the set of all positive real numbers.
Answer:
Hence, the correct answer is option (b) (reals, positive reals).
The given set is {(x,y) : Y = x2}. This represents a parabola in the Cartesian plane. The domain of this set is the set of all real numbers, because for any real value of x, we can find a corresponding value of y (x2) which belongs to the set.
The range of this set is the set of all positive real numbers, because y (x2) is always greater than or equal to zero, and can take on any positive value. Therefore, the range of the set is the set of all positive real numbers.
Answer:
Hence, the correct answer is option (b) (reals, positive reals).
Community Answer
The domain and range of {(x,y) : Y = x2} isa)(reals, natural numbers)b...
- The set (x, y) where y = x^2 represents a parabola opening upwards.
- Domain: All real numbers (x) can be any real number.
- Range: Since y = x^2, y is always non-negative. The smallest value y can take is 0 (when x = 0). Thus, the range is all non-negative real numbers.
- Domain: All real numbers (x) can be any real number.
- Range: Since y = x^2, y is always non-negative. The smallest value y can take is 0 (when x = 0). Thus, the range is all non-negative real numbers.
- Option B would have been the correct answer if the range did not have 0 in it.
-Therefore,
- Option B, although identifies the domain as reals and the range as positive reals, but actually includes 0. So, technically, "none of these" fits better.
- Option B, although identifies the domain as reals and the range as positive reals, but actually includes 0. So, technically, "none of these" fits better.
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The domain and range of {(x,y) : Y = x2} isa)(reals, natural numbers)b)(reals, positive reals)c)(reals, reals)d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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