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

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Answer 1 · 2018-07-22T05:29:40

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

#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]#