SOLUTION: Determine the domain of f in f(x)=10-square root of 3-x

Question 330567: Determine the domain of f in f(x)=10-square root of 3-x
Answer by nyc_function(2741) (Show Source): You can put this solution on YOUR website!
We have f(x) = 10 - sqrt[3 - x].
Set what lies in the radicand to be greater than or equal to zero and then solve for x.
3 - x ≥ 0
-x ≥ -3
Since we are dividing by a negative number, the inequality sign must by reversed.
x ≤ -3/-1
x ≤ 3
This makes sense because any number bigger than 3 that we replace x with in the radicand will make your square root undefined.
The domain is: ALL REAL NUMBERS EXCEPT THAT X MUST BE LESS THAN OR EQUAL TO 3.

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