How do you find the domain and range of #root4(9-x^2)#?

1 Answer
Aug 1, 2017

Answer:

Domain : #-3 <= x <= 3# or #[-3, 3]#
Range: # 0 <= f(x) <= sqrt3 or [0,sqrt3] #

Explanation:

# f(x)=root(4) (9-x^2) # . For domain under root must be # >=0 #

#:. 9-x^2 >= 0 or x^2 <= 9 :. x <= 3 or x>= -3#

Domain : #-3 <= x <= 3# or #[-3, 3]#

Range : Minimum value : #f(x)=0# when # x = +-3# and

maximum value : #f(x)=sqrt ((sqrt (9) ) )= sqrt 3 # when # x = 0#

Range: # 0 <= f(x) <= sqrt3 or [0,sqrt3] #

graph{(9-x^2)^0.25 [-10, 10, -5, 5]} [Ans]