SOLUTION: determine the domain of the function f(x)=sqrt of 3-x

Question 140040: determine the domain of the function f(x)=sqrt of 3-x
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 3 from both sides

Combine like terms on the right side

Divide both sides by -1 to isolate x (note: Remember, dividing both sides by a negative number flips the inequality sign)

Divide

So that means x must be less than or equal to in order for x to be in the domain

So the domain in set-builder notation is

So here is the domain in interval notation: (-

,3]

Notice if we graph , we get
notice how the graph never crosses the line

and we can see that x must be less than or equal to in order to lie on the graph. So this graphically verifies our answer.

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