How do you find the domain and range of #f(x) = -2 * sqrt(x-3) + 1#?

1 Answer
Jun 20, 2017

Answer:

Domain: #x>=3# In interval notation : # [3,oo)#
Range: #f(x)<= 1 #. In interval notation : # (-oo,1]#

Explanation:

#f(x) = -2*sqrt(x-3)+1 #

Domain: Under root should be #>=0 :. x-3>=0 or x>=3#

Domain: #x>=3# In interval notation : # [3,oo)#

Range: When #x=3 ; f(x)= 1#. For #x>3 ; f(x)# goes on decreasing.

Range: #f(x)<= 1 #. In interval notation : # (-oo,1]#

graph{-2*(x-3)^0.5+1 [-10, 10, -5, 5]} [Ans]