How do you decide whether the relation #xy+7y=7# defines a function?

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Answer 1 · 2015-11-09T05:00:25

You can rearrange the expression to find that #y# is uniquely determined in terms of #x#, therefore a function.

#7 = xy + 7y = (x+7)y#

Notice that if #x = -7# then there are no solutions, since this results in #7 = 0y = 0#.

If #x != -7# then we can divide both sides by #x+7# to get:

#7/(x+7) = y#

That is:

#y = 7/(x+7)#

This uniquely determines the value of #y# for any value of #x# apart from #x=-7#, where it is not defined.