What is the domain and range of #F(x) = 5/(x-2)#?

1 Answer
Mar 11, 2018

Answer:

#text(Domain): x!=2#
#text(Range): f(x)!=0#

Explanation:

The domain is the range of #x# values which give #f(x)# a value that is unique, such there is only one #y# value per #x# value.

Here, since the #x# is on the bottom of the fraction, it cannot have any value such that the whole denominator equals zero, i.e. #d(x)!=0# #d(x)=text(denominator of the fraction that is a function of)# #x#.

#x-2!=0#
#x!=2#

Now, the range is the set of #y# values given for when #f(x)# is defined. To find any #y# values that cannot be reached, i.e. holes, asymptotes, etc. We rearrange to make #x# the subject.

#y=5/(x-2)#

#x=5/y+2#, #y!=0# since this would be undefined, and so there are no values of #x# where #f(x)=0#. Therefore the range is #f(x)!=0#.