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

1 Answer

Answer:

#x<=4, y>=0#

Explanation:

The domain of a function is the set of all allowable #x# values. What are the allowable values of #x# in the equation #f(x)=sqrt(4-x)#? Keep in mind that, in general, we don't allow values inside a square root sign to be negative. So our allowable values of #x# are:

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

The range of a function is the set of #y# values associated with the domain. What are the resulting values of #y#? We know that, with #x=4, y=0# and that is the lowest value of #y# we'll have. As #x# increases, #y# will increase also, albeit far more slowly. And so our range is:

#y>=0#