SOLUTION: Find the domain of f(x)= 7+ the square root of 3x+21, and express it using interval notation.

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Question 102559This question is from textbook Algebra and Trigonometry
: Find the domain of f(x)= 7+ the square root of 3x+21, and express it using interval notation. This question is from textbook Algebra and Trigonometry

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
y=7%2Bsqrt%283x%2B21%29 Start with the given expression

Remember you cannot take the square root of a negative value. So that means the argument 3x%2B21 must be greater than or equal to zero (i.e. the argument must be positive)

3x%2B21%3E=0 Set the inner expression greater than or equal to zero

3x%3E=0-21Subtract 21 from both sides


3x%3E=-21 Combine like terms on the right side


x%3E=%28-21%29%2F%283%29 Divide both sides by 3 to isolate x



x%3E=-7 Divide


So that means x must be greater than or equal to -7


So here is the domain in interval notation: [-7,)


Notice if we graph y=7%2Bsqrt%283x%2B21%29 , we get
+graph%28+500%2C+500%2C+-10%2C+10%2C+-2%2C+18%2C+7%2Bsqrt%283x%2B21%29%29+ notice how the graph never crosses the line x=-7. So this graphically verifies our answer.

and we can see that x must be greater than or equal to -7 in order to lie on the graph