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

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) (Show Source): You can put this solution on YOUR website!
Start with the given expression

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

Set the inner expression greater than or equal to zero

Subtract 21 from both sides

Combine like terms on the right side

Divide both sides by 3 to isolate x

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 , we get
notice how the graph never crosses the line . 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

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