How do you find the domain and range of #f(x) = -sqrt(2x + 4) + 3#?

1 Answer
Jul 2, 2018

Answer:

Domain: #x >= -2 or [-2, oo)#
Range: #f(x) <= 3 or [3, -oo)#

Explanation:

#f(x) = -sqrt (2 x+4)+3#

Domain : Possible input of #x#. Under root is undefined at #<0#,

so it must be #>=0 :. 2 x +4 >=0 or 2 x >= -4 or x >= -2#

Domain: #x >= -2 or [-2, oo)#

Range: Possible output value of #f(x) ; sqrt (2 x+4)>=0#.

Range: #f(x) <= 3 or [3, -oo)#

graph{-(2 x+ 4)^0.5+3 [-10, 10, -5, 5]} [Ans]