SOLUTION: State the domain of the following function using interval notation. f(x)=sqrt(-x^2+8x-15) I got (-3, infinity) and its wrong. Thank you in advance

Question 1051629: State the domain of the following function using interval notation. f(x)=sqrt(-x^2+8x-15) I got (-3, infinity) and its wrong. Thank you in advance
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
-x^2+8x-15 must be greater than or equal to 0
The function multiplied by -1 is x^2-8x+15 and factors into (x-5)(x-3)
Those are the 0 points.
One can test the function in 3 places, less than 3, between 3 and 5, and greater than 5.
Try x=0 and f(x)=-15, so the first one doesn't work
Try x=4 and -16+32-15 does work, so the area between works.
Try x=6 and -36+48-15 does not work.
[3,5]
Graphing helps look at where the function is positive.

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