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Mathematics
OpenStudy (anonymous):

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

OpenStudy (anonymous):

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

OpenStudy (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.

OpenStudy (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, \[\infty\] )

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