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

1 Answer
Jun 27, 2018

Answer:

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

Explanation:

#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]}