How do you find the domain and range of # 1/(x+2)#?

1 Answer
Aug 16, 2017

Answer:

Domain: #(-oo,-2)uu(-2,+oo)#
Range: #(-oo,0) uu (0,+oo)#

Explanation:

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

#f(x)# is defined #forall x in RR# except #x=-2#

Hence, the domain of #f(x)# in interval notation is# (-oo, -2)uu(-2, +oo)#

Consider #lim_(x->-2-) = -oo#

And #lim_(x->-2+) = +oo#

Also, #f(x) != 0# for any finite #x#

Hence, the range of #f(x)# is #(-oo,0) uu (0,+oo)#

As can be seen by the graph of #f(x)# below.

graph{1/(x+2) [-10, 10, -5, 5]}