Question

what is the domain if the range is all real numbers? f(x) = the square root of 6-x

Answer 1

\[\sqrt{6-x}\]

Answer 2

close but no

Answer 3

you claim the domain is x <= -6, but I can plug in x = 0

y = sqrt(6 - x)

y = sqrt(6 - 0)

y = sqrt(6)

and I get a real number just fine. So that's not the whole domain.

Answer 4

you need to solve 6-x >= 0 for x

Answer 5

it sounds like you're guessing at this point

Answer 6

solve 6-x >= 0 for x

if you multiply both sides of the inequality by a negative number, then the inequality sign will flip

if you divide both sides of the inequality by a negative number, then the inequality sign will flip

Answer 7

so thats x>=6

Answer 8

no

Answer 9

why not add x to both sides

Answer 10

that may be easier

Answer 11

6-x>=0
-6 -6
---------
-x>-6
-- ----
-1 -1
x<=6

Answer 12

correct

Answer 13

yes I already said "correct" above lol