What is the domain and range of #f(x)=sqrt(16-x^3)#?

1 Answer
Binayaka C.
May 13, 2017

Domain: #x <= root(3)16 or (-oo , root(3)16]#
Range: #f(x) >=0 or [0,oo)#

Explanation:

#f(x)=sqrt(16-x^3) # Domain: under root should not be negative , so
#16-x^3 >=0 or 16 >= x^3 or x^3 <= 16 or x <= root(3)16#

Domain: #x <= root(3)16 or (-oo , root(3)16]#

Range: #f(x)# is any real value #>=0#

Range: #f(x) >=0 or [0,oo)#
graph{(16-x^3)^0.5 [-10, 10, -5, 5]}

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