How do you find the domain and range of #f(x) = 1 / (x-5)#?

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Answer 1 · 2017-02-04T14:27:45

The domain is #D_f(x)=RR-{5}#
The range is #R_f(x)=RR-{0}#

As you cannot divide by #0#, #x!=0#

So, the domain of #f(x)# is #D_f(x)=RR-{5}#

Let #y=1/(x-5)#

#y(x-5)=1#

#yx-5y=1#

#yx=1+5y#

#x=(1+5y)/y#

Therefore,

#f^-1(x)=(1+5x)/x#

The range of #f(x)# #=# the domain of #f^-1(x)#

The domain of #f^-1(x)# is #D_(f^-1(x))=RR-{0}#

The range of #f(x)# is #R_(f(x))=RR-{0}#