SOLUTION: How to find the domain of f o g and g o f if f(x)=(3x+2)^1/2 and g(x)=x^2+3

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Question 752691: How to find the domain of f o g and g o f if f(x)=(3x+2)^1/2 and g(x)=x^2+3
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Form the compositions and judge from those.

f o g:

=%283x%5E2%2B9%2B2%29%5E%281%2F2%29=%283x%5E2%2B11%29%5E2
highlight%28f%28g%28x%29%29=%283x%5E2%2B11%29%5E%281%2F2%29%29

What can the values of x be and what must not be allowed for the values of x?
No restriction for f(g(x)). All real numbers are allowed.

How about g(f(x))?