SOLUTION: whats is the domain of f(x)= fourth root of x^2 + 3x

Question 212291This question is from textbook
: whats is the domain of
f(x)= fourth root of x^2 + 3x This question is from textbook

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
whats is the domain of
f(x)= fourth root of x^2 + 3x
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f(x) = (x^2 + 3x)^(1/4)
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To get Real Number results x^2+3x must be non-negative.
x^2+3x >= 0
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x(x+3) >= 0
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Draw a number line.
Plot x = -3 and x=0
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Test a value in each resulting interval to see where the solutions are:
If x = -10 you get -10(-7) >= 0, true, so solutions in (-inf,-3]
If x = -1 you get -1(2) >= 0, false
If x = 10 you get 10(13)>= 0, true, so solutions in [0,+inf)
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Cheers,
Stan H.
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