What is the domain and range of Q(s)=1/(sqrt(2s))Q(s)=12s?

1 Answer
Jun 27, 2018

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

Explanation:

Q(s) = 1/sqrt(2s)Q(s)=12s

Q(s)Q(s) is defined for sqrt(2s) !=02s0

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]}