Question 330567
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.