Question

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

Answer 1

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)`