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the domain will contain all those numbers for which the quantity under \(\sqrt .. \) will be non-negative.
HINT: \(3x +4 \ge 0\)
yes, it does. set (3x+4)=0 solve for x anything greater than that will result in a positive under the radical anything less than that will result in a negative under the radical negative under the radical means imaginary, doesn't exist therefore not part of the domain

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Other answers:

-5 won't matter just exclude the numbers for whic 3x+4 <0
@geerky42 thank you
You're welcome.

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