Find the domain of the function f,defined by f(x)=√x^(3) (9-x)?

Question

# f(x)={x^(3) (9-x)}^(1/2)#

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Answer 1 · 2018-04-15T04:37:17

This is the Domain of the function :-

#D_f : ##0<=x<=9#

NOTE that the term inside the square root MUST be Positive so these are the two necessary conditions for the function to be defined :-

#1)# First :-

#9-x>=0 #

#rArr x<=9#

#2)# Second :-

#x^3 >=0#

#rArr x>=0#

Now taking the intersection #∩ # of the above two conditions we get the domain of the function :-

#:. D_f : ##0<=x<=9#

The graph of this function is shown below :-