Question #eacc1

1 Answer
Jim S
Jan 7, 2018

#f# continuous in #D_f#

Explanation:

#f(x)=ln((x-1)/(x+1))#

#D_f={AA##x##in##RR#: #(x-1)/(x+1)>0# , #x+1!=0##}# #=#

#{(x-1)(x+1)>0#, #x!=-1}# #=# #(-oo,-1)uu(1,+oo)#

  • #f# is continuous in each of the intervals #(-oo,-1)# , #(1,+oo)# as composition of basic continuous functions, #g(x)=(x-1)/(x+1)# , #h(x)=lnx#

NOTE: All this of course, if you're referring to #ln((x-1)/(x+1))# and not #ln(x-1/x+1)#

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