How do you find the domain and range of # f(a)=3sqrt(4a)#?

1 Answer
Jun 30, 2016

Answer:

Assuming we are restricted to Real numbers:
#"Domain"_f=[0,+oo)#
#"Range"_f=[0,+oo)#

Explanation:

#3sqrt(4a)# is defined as a Real number for all values of #(4a) >= 0#
which implies for all values of #a>=0#
Thus the domain is #[0,+oo)#

The minimum value of #3sqrt(4a)# is #0# which occurs when #a=0# and increases without bound as #ararr+oo#
Thus the range of #f(a)=3sqrt(4a)# is #[0,+oo)#