What is the domain and range of #F(x) = 7/(6x-5)#?

1 Answer
Sep 8, 2015

Answer:

Domain: #x inRR, x!=5/6#
Range: #F(x)in RR, F(x)!=0#

Explanation:

#F(x) = 7/(6x-5)# is not defined if #(6x-5)=0# (i.e. if #x=5/6#

therefore #x=5/6# must be excluded from the Domain

Consider the partial inverse equation:
#F(x) = 7/(6x-5)#
#rarr 6x-5 = 7/F(x)#

This will not be defined if #(F(x)=0#
therefore #F(x) =0# must be excluded from the range.
graph{7/(6x-5) [-20.27, 20.26, -10.13, 10.15]}