How do you find the domain of # sqrt{-x - 2}#?

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Answer 1 · 2016-06-19T05:26:32

All values of x smaller than or equal to -2 (or #x<=-2#)

Domain of #sqrt(f(x))# is always all values of x for which #f(x)>=0# as if #f(x)# is negative, #sqrt(f(x))# is no longer real.

Thus, here #f(x)=-x-2#

#f(x)>=0# which means that #-x-2>=0#

Adding 2 on both sides, we get
#-x>=2#

If we multiply -1 on both sides, we'll have to reverse the sign of inequality, so this becomes

#x<=-2#

Hence for all values of x smaller than or equal to -2, #sqrt(-x-2)# will be real and hence, these values are the domain for this function.