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f(x)=4x/2x+1

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I think the problem is 4x/(2x+1).  If that's not right, let me know.
 
Without other restrictions, the domain of a function is the set of all values for the independent variable x for which the function makes sense.  
 
In this case I assume we are limiting the domain values to the real number line - so that is one restriction.
 
the function 4x/(2x+1)  makes sense for every real number x for which the denominator 2x+1 is not zero. Which means 2x ≠ -1, so x ≠ -1/2.  
 
So the domain is (-infinity,-1/2) union (-1/2,infinity).  That is, the domain is every real number except -1/2.