Find the domain of the given function.

f(x) = sqrt. x+6/{(x+7)(x-9)}

Question

Find the domain of the given function.

f(x) = sqrt. x+6/{(x+7)(x-9)}

anonymous · Answer

Is your question to find the domain of  $$\sqrt{\frac{ x+6 }{ (x+7)(x-9) }}$$

anonymous · Answer

no the sqrt is only on the top 
@calmat01

anonymous · Answer

ok

anonymous · Answer

So, you know that you cannot take square roots of negative numbers, correct?

anonymous · Answer

right

anonymous · Answer

And you also know that you cannot divide by zero, right?

anonymous · Answer

yes

anonymous · Answer

Alright, so now, all we have to do is make sure the x's we use satisfy the two situations.  Namely, x+6>=0 and also x+7 cannot be zero nor can x-9 by zero.

anonymous · Answer

what?

anonymous · Answer

so x can not be = to 7,6, and 9?

anonymous · Answer

Not quite, but close.  Since $$x+6\ge0$$ because we cannot take the sq. rt of a negative number, the first thing we know is that x must be greater than or equal to -6.

Now since x+7 =0 when x=-7, I can't use that value because we have already established that x must be greater than or equal to -6.  

Finally, x-9=0 when x=9, so you can use any number less than 9 but greater than or equal to -6, and you can use any number greater than 9.

Put all of that together, and your domain is $$[-6,9)\cup\left( 9, \right)$$