SOLUTION: Find the domain and range of square roott x^3-8x

Question 56606This question is from textbook
: Find the domain and range of
square roott x^3-8x This question is from textbook

Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Find the domain and range of
square roott x^3-8x
since square root is involved
x^3-8x>=0
x(x^2-8)>=0
(x+SQRT8)x(x-SQRT8)>=0...the zeros in increasing order are -SQRT8,0,SQRT8
for the product to be positive or zero
1.x>=SQRT8...that is [SQRT8,infinity)
2.x>=-SQRT8 but <=0......that is (-SQRT8,0)
hence domain is (-SQRT8,0) and [SQRT8,infinity)
correspondingly the range is 0 to infinity since as a rule we take only the positive value of squareroot.
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