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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...
Domain and Range of a Function
Domain: The set of all possible input values (x-values) for a function.
Range: The set of all possible output values (y-values) for a function.
Explanation
The given function is Y = x2. Let's find the domain and range of this function.
Domain:
The input values (x-values) for this function can be any real number. Therefore, the domain of this function is all real numbers.
Range:
The output values (y-values) for this function are the square of the input values. Since the square of any real number is always positive, the range of this function is all positive real numbers.
Therefore, the correct answer is option 'B' - (reals, positive reals).
Domain: The set of all possible input values (x-values) for a function.
Range: The set of all possible output values (y-values) for a function.
Explanation
The given function is Y = x2. Let's find the domain and range of this function.
Domain:
The input values (x-values) for this function can be any real number. Therefore, the domain of this function is all real numbers.
Range:
The output values (y-values) for this function are the square of the input values. Since the square of any real number is always positive, the range of this function is all positive real numbers.
Therefore, 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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