How do you find the domain and range of #y = 3/x^2#?

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Answer 1 · 2017-04-26T09:12:49

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

#y=3/x^2#

#y# is defined #forall x in RR: x!=0#

Hence the domain of #y# is #(-oo, 0) uu (0,+oo)#

Consider both:

#lim_"x->+-0" 3/x^2 = oo#

and
#lim_"x->+-oo" 3/x^2 = 0#

Hence the range of #y# is #(0, +oo)#

These can be seen from the graph of #y# below:

graph{3/x^2 [-6.967, 7.08, -0.73, 6.294]}