How do you find the domain of # f(x) = - sqrt(7-x)#?

1 Answer
Oct 6, 2016

square roots can't be negative in real numbers, so find the zero of the radical and test left and right. graph{-sqrt(7-x) [-10, 10, -5, 5]}


Domain: all x's that work. Range: all possible y's
Then think: what values for x make the radical come out greater than or equal to zero? 7 makes it zero, so the domain is x is less than or equal to 7, because those are all the x's that work. (8,9, etc make it negative. Substituting numbers in can help the process.
If you must do set notation, x is from negative infinity to 7, including 7. Sorry, don't have set notation up. (closed bracket on the 7)
The range would be negative infinity to 0, closed bracket on 0, fyi.