What is the range of #f(x) = 3/(x-2)+1# ?

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Answer 1 · 2017-05-03T03:24:03

#(-oo,+oo)#

#f(x) = 3/(x-2)+1#

#f(x)# is defined for all #x# except #x=2#
That is #forall x: (x!=2)#

Thus the domain of #f(x)# is: #(-oo, 2)uu(2, +oo)#

The #lim_(x->2^-) f(x)= -oo# and #lim_(x->2^+) f(x)= oo#

Thus the range of #f(x)# is: #(-oo,+oo)#

This can be seen from the graph of #f(x) below.

graph{3/(x-2)+1 [-16, 16.04, -8.01, 8]}