Question #123b8

1 Answer
Aug 12, 2017

#{x in RR: -6<= x <= 1}#

Explanation:

In the realm of real numbers, the radicand must be positive (the square root of negative numbers is a nonreal quantity).

We can factor the radicand into

#ul(sqrt(-(x+6)(x-1))#

We see that the function equals #0# when #x = -6# and #x = 1#, so what we need to do is figure out if the domain is real in between these two numbers or outside of these values.

Plugging in a value between #-1# and #6# (let's say #0#):

#-(0+6)(0-1) = color(red)(6#

Since it is positive, we know the domain is at least

#-6<= x <= 1#

Plugging in #-7# and #2# yields

#-(-7+6)(-7-1) = -8#

#-(2+6)(2-1) = -8#

Since these are both negative, our final domain is

#color(blue)(ulbar(|stackrel(" ")(" "{x in RR: -6<= x <= 1}" ")|)#

(The domain is all real numbers such that #x# is greater than or equal to #-6# and less than or equal to #1#).