How do you find the domain of #f(x)=sqrt(4-x)#?

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Answer 1 · 2016-07-07T08:11:15

#Df(x) = x in R ; x > 4#

The domain is the set of #x#-values that can be used to draw the function so,

You are unable to get a square-root of a negative number therefore the value under the square root must be #>= 0#.

Therefore we need all of the #x#-values that result in the value of #4 - x# being #>= 0#.

#4 -x >= 0#
#4 >= x#
#x <= 4#

So all #x#-values #<= 4# will work in the equation. Now we right this in terms of all real numbers:

The Domain of #x# is all the real numbers expect when #x > 4# (This produces a negative under the square root)

#Df(x) = x in R ; x > 4#