What is the domain and range of #y = 1/(x - 2)#?

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Answer 1 · 2018-03-10T13:08:52

Domain: #(-oo,+2)uu(+2,+oo)#
Range: #(-oo,+oo)#

#y =1/(x-2)#

#y# is defined for all #x in RR:x!=+2#

Hence, The domain of #y# is #(-oo,+2)uu(+2,+oo)#

Consider:

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

Hence, the range of #y# is #(-oo,+oo)#

As can be deduced from the graphic of #f(x)# below:

graph{1/(x-2) [-16.01, 16.02, -8.01, 8]}