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Consider the following relation R defined by the equation:R = {(x, y) | y = 2x + 1}The above relation is a function with a domain and codomain specified as follows:Domain: {1, 2, 3, 4, 5}Codomain: {3, 5, 7, 9, 12}

Question

Consider the following relation R defined by the equation:R = {(x, y) | y = 2x + 1}The above relation is a function with a domain and codomain specified as follows:Domain: {1, 2, 3, 4, 5}Codomain: {3, 5, 7, 9, 12}

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Solution

The given relation R is defined by the equation y = 2x + 1. This is a linear equation, and it describes a function because for every input x, there is exactly one output y.

The domain of a function is the set of all possible input values, which in this case is given as {1, 2, 3, 4, 5}.

The codomain of a function is the set of all possible output values. Here, it is given as {3, 5, 7, 9, 12}.

We can find the actual output values (range) of the function by substituting the domain values into the function equation:

For x = 1, y = 21 + 1 = 3 For x = 2, y = 22 + 1 = 5 For x = 3, y = 23 + 1 = 7 For x = 4, y = 24 + 1 = 9 For x = 5, y = 2*5 + 1 = 11

So, the actual output values or the range of the function is {3, 5, 7, 9, 11}.

Comparing this with the given codomain, we see that the value 11 is not in the codomain and the value 12 is not in the range. Therefore, the given codomain does not match the range of the function for the given domain.

This problem has been solved

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