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Question 147117: State the domain of f(x)= squareroot x-8 and provide a brief explanation
I am not sure what to do for this question
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Think of a function as a little box with a slot on one end and a hopper on the other. You put numbers into the slot ( ) and you get the value of the function ( ) in the hopper. Some functions let you put any number you want in the slot, but others come with a warning label that tells you that certain numbers will cause that particular function machine to malfunction. Mathematically speaking, you have to exclude any value that makes the function undefined. Typically, this would be any value of that would cause a division by zero, or having the value under a radical be less than zero (the square root of a negative number is not defined in the real number system)
The domain of a function is that set of values that is allowed. In other words, take the real numbers, eliminate those values you can't use in the function, and the domain is what is left.
In the case of your function, you have no division operation so you don't have to worry about division by zero, but you do have a radical and you have to make sure that the expression under the radical is always greater than or equal to zero.
So, if  , we have to make sure that  , or  . So the domain is the set of all real numbers such that . You can express it in set builder notation: { | is real and } or interval notation: [ , ).
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