Question 72904
Given:
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{{{f(x)=4^x/4^x+2}}}
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I'm not sure whether you intended the problem to be as shown in the next line up.  But by the
rules that govern the order in which math operations are done, that's the way it translates.
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Note that {{{4^x/4^x = 1}}} so f(x) reduces to:
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{{{f(x) = 1 + 2}}}
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and this further reduces to 
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{{{f(x) = 3}}}
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Notice that there are no terms involving x on the right side, so whatever x is assumed to
be the answer for f(x) is always 3.
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Because of this {{{f(1/2006) = 3}}} and {{{f(2005/2006) = 3}}}.  So:
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{{{f(1/2006) + f(2005/2006) = 3 + 3 = 6}}}
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That was painless. I guess the teacher was just trying to make a point about how the order
of operations is important because this problem could have much more difficult if you read
the line equation wrong for f(x).
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Hope this helps you see how the order of operations in the equation you provided should be 
interpreted as shown at the top of this reply.