Answer :
Final answer:
The mapping g is not a function because an element 'b' from the domain is mapped to two different elements in the codomain. Therefore, g is not a function, nor is it a one-to-one, onto or a bijection function. The only correct answer is 'g is a function that is neither one-to-one nor onto'.
Explanation:
The mapping in question, g, is a set of ordered pairs. A function is defined such that each element from the first set (the domain) is paired with exactly one element from the second set (the codomain). Looking at the pairs for g, we see that 'b' from the domain D is paired with both 7 and 5 from the codomain E. This means that g is not a function, because 'b' doesn't point to a unique element in E.
An onto function (or surjective function) is a function in which every element of the codomain is the image of at least one element of the domain. Here, 7 and 8 from E are not mapped by any element from D, so g isn't an onto function.
A one-to-one function (or injective function) is a function where no two elements of the domain are mapped to the same element of the codomain. Since 'b' is mapped to both 5 and 7 in E, g isn't a one-to-one function. A bijection is a function that is both one-to-one and onto, so g cannot be a bijection because it isn't either.
In conclusion, g is not a function. Options 'g is an onto function', 'g is not a function', 'g is a bijection', and 'g is a one-to-one function' are all incorrect when referring to g. The correct option is 'g is a function that is neither one-to-one nor onto'.
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