How do you find the domain and range of # f(x)=(x+2)/(x-2)#?

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Answer 1 · 2017-04-27T09:02:30

The domain of #f(x)# is #RR-{2}#
The range of #f(x)# is #RR-{1}#

As we cannot divide by #0#, #x!=2#

The domain of #f(x)# is #D_f(x)=RR-{2}#

Let #y=(x+2)/(x-2)#

Then,

#yx-2y=x+2#

#yx-x=2y+2#

#x(y-1)=2(y+1)#

#x=2(y+1)/(y-1)#

Therefore,

#f^-1(x))=2(x+1)/(x-1)#

The domain of #x# is the range of #y#

The range of #f(x)# is #R_f(x)=RR-{1}#

graph{(y-(x+2)/(x-2))(y-1)=0 [-9.25, 10.75, -2.93, 7.07]}