How do you find the domain and range of y = 5 - sqrt(9-x^2)?

1 Answer
Jul 22, 2018

Dx=[-3;3] and R=[2;5]

Explanation:

y=5-sqrt(9-x^2)

domain sqrt(m) then dom=m>=0

sqrt(9-x^2)>=0

9-x^2>=0

x^2-9<=0

(x-3)(x+3)<=0

x=-3; x=3

negative zone

-3<=x<=3 -> x ∈ [-3;3]

Range from domain

-3<=x<=3

elevating to square

0<=x^2<=9

multiply -1

0>=-x^2>=-9

add 9

9>=9-x^2>=0

square root

3>=sqrt(9-x^2)>=0

multiply -1

-3<=-sqrt(9-x^2)<=0

add 5

2<=5-sqrt(9-x^2)<=5

2<=y<=5

Range y ∈ [2;5]