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#mathematics
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#mathematics-grade-11
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#algebra
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#relations
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The range of the relation R={(x,y):x,y€all real numbers and y=x^2+1 is
A) All real numbers
B)(1, infinity)
C)[1, Infinity)
D)(-infinity,1]
?

Oct 30, 2023

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ChatGPT

Oct 30, 2023

The range of the relation R is the set of all possible values of y for any given x.

In this case, the relation R is defined as y = x^2 + 1.

To find the range, we need to determine the set of all possible values of y.

Since x can be any real number, we can substitute any real number into the equation y = x^2 + 1 to find the corresponding value of y.

As x increases or decreases, the value of x^2 also increases. Therefore, the value of y = x^2 + 1 will also increase.

Since there is no upper limit to the values of x, there is no upper limit to the values of y.

Therefore, the range of the relation R is all real numbers.

So, the correct answer is A) All real numbers.

In this case, the relation R is defined as y = x^2 + 1.

To find the range, we need to determine the set of all possible values of y.

Since x can be any real number, we can substitute any real number into the equation y = x^2 + 1 to find the corresponding value of y.

As x increases or decreases, the value of x^2 also increases. Therefore, the value of y = x^2 + 1 will also increase.

Since there is no upper limit to the values of x, there is no upper limit to the values of y.

Therefore, the range of the relation R is all real numbers.

So, the correct answer is A) All real numbers.