The range of the function in the first photo is x-3>=0 sqrt(x-3)>=sqrt(0) sqrt(x-3)>=0 Multiplying the equation by -2: -2[ sqrt(x-3)>=0] -2 sqrt(x-3)<=0 Adding 8 both sides of the equation: -2 sqrt(x-3)+8<=0+8 -2 sqrt(x-3)+8<=8 f(x)<=8 Then Range f(x)= (-Infinite, 8]
The function has the same range is the third one: g(x)=-sqrt(x+3)+8
The range of this function is: x+3>=0 sqrt(x+3)>=sqrt(0) sqrt(x+3)>=0 Multiplying the equation by -1: -1[ sqrt(x+3)>=0] - sqrt(x+3)<=0 Adding 8 both sides of the equation: - sqrt(x+3)+8<=0+8 - sqrt(x+3)+8<=8 g(x)<=8 Then Range g(x)= (-Infinite, 8]
