Question

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

Answer 1

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

Answer 2

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.

Answer 3

\[\sqrt{(-6x-9)}\] 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, \[\infty\] )