What is the domain and range of #Q(s)=1/(sqrt(2s))#?

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Answer 1 · 2018-06-27T12:45:43

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

#Q(s) = 1/sqrt(2s)#

#Q(s)# is defined for #sqrt(2s) !=0#

Assuming #Q(s) in RR -> 2s>=0#

Thus #s>0#

#:.# the domain of #Q(s)# is #(0,+oo)#

Consider:

#lim_(s->+oo) Q(s) = 0 and lim_(s->0) Q(s) -> +oo#

#:.# the range of #Q(s)# is also #(0,+oo)#

We can deduce these results from the graph of #Q(s)# below.

graph{1/sqrt(2x) [-3.53, 8.96, -2.18, 4.064]}