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Given that g is defined on all of R, define the set g^(-1)(B) for a subset B of R.

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Final answer:

The set g^(-1)(B) is the preimage of subset B under the function g, consisting of all x in R such that g(x) is an element of B.

Step-by-step explanation:

The student's question pertains to the definition of the preimage of a subset B under a function g. When g is defined on all of R (the set of all real numbers), g^(-1)(B) represents the set of all elements x in R such that when g is applied to x, the result is an element of subset B. In other words, if we input x into our function g, the output is in B. So, the set g^(-1)(B) consists of all the inputs that, when the function g is applied, will give outputs that are in B. It's essentially asking which numbers you could put into the function to get results that are in the set B.

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