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Question 26640: find the domain of the function
f(x)=x+6-(square root of x+2)
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3x-1/2
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! to be honest, looking at the "function"... the existence of the square root means that the fundamental definition of what a function is may well be broken by this. In short, i do not believe this is a function, strictly.
However, putting that aside! What values of x are we allowed to put into the equation? Well avoid anything that makes the square root negative is nothing less than x=-2. Also the denominator should not be zero: when it is, the equation will become infinite..an asymptote.
This happens when 3x-(1/2) = 0
--> 3x = 1/2
--> x = 1/6
So, at a first glance the domain is any real value of x greater or equal to -2 but not 1/6.
Ask your teacher though to clarify if this is really a function! I think it isn't :-)
jon.
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