## anonymous 4 years ago Find the domain of the following function. State your answer in interval notation. Please show all of your work f(x)= -10x-3 ------------- Find the domain of the following function. State your answer in interval notation. Please show all of your work f(x)= -10x-3 ----------- √-6x-9+x

1. anonymous

does posting a link to openstudy.com count as showing all your work?

2. anonymous

the domain does not include places where the square root is negative, and it also skips points where the denominator evaluates to 0. otherwise all the x-values are fair game.

3. anonymous

$\sqrt{(-6x-9)}$ means -6x-9 cannot be negative $\ge 0$ add 9 to both sides, and divide by -6 x $\le$ -3/2 The whole denominator cannot = 0 $\sqrt{(-6x-9)} +x$ = 0 subtract x on both sides $\sqrt{(-6x-9)} =-x square both sides -6x-9 = x^2 Get equation = 0 x^2 + 6x + 9 = 0 Factor and solve (x + 3)(x + 3) = 0 x+3 = 0 x = -3 Therefore x is any real number except -3. (-\[\infty$, -3) $\cup$ (-3, $\infty$ )