How do you find the domain and range of #y = sqrt(x-10) + 5#?

1 Answer

Answer:

Refer to explanation

Explanation:

Well we have that

#y=f(x)=sqrt(x-10)+5=#

since we have a square root the quantity under it must equal or greater than zero hence

#x-10>=0=>x>=10#

So the domain is #[10,+oo)# (where x gets its values)

To find the range eg where y gets its values we notice that

#y-5=sqrt(x-10)>=0=>y-5>=0=>y>=5# hence the range is

#[5,+oo)#