Which is the domain and range of f(x) = -3sqrt (x+2) - 6?

1 Answer
Jul 17, 2018

Domain: x>=-2 or [-2,oo)
Range : f(x) <= -6 or (-oo,-6]

Explanation:

f(x)= -3 sqrt(x+2) - 6 . Domain: Possible input value of x.

Under root should be >0 ; f(x) is undefined at x+2<0

:. x+2>=0 or x >= -2 . Therefore domain is

x>=-2 or [-2,oo) . Range: Possible output of f(x)

for input x ; sqrt(x+2)>=0:. f(x) <= (-3*0) -6 :.

Range : f(x) <= -6 or (-oo, -6]

graph{-3 sqrt(x+2) -6 [-40, 40, -20, 20]} [Ans]