Homework Help Forum: Algebra

Posted by Jena on Thursday, February 3, 2011 at 7:32pm.


Find the domain of the function.
f(x)=(sqrt x+6)/(-2x-5)

Write your answer as an interval or union of intervals.

Algebra - David, Thursday, February 3, 2011 at 7:42pm
(-6,-5/2)and(-5/2,infinity)

Algebra - Reiny, Thursday, February 3, 2011 at 7:46pm
the simplest way to describe the domain:

x ? -6 , x ? -5/2

Algebra - Jena, Thursday, February 3, 2011 at 7:52pm
I'm lost

For the domain, the denominator can't equal zero.

-2x - 5 = 0
-2x = 5
x = -5/2

So, x cannot equal -5/2
All x not equal to -5/2

For the numerator, you cannot have a negative inside the square root.

x + 6 >= 0
x >= -6

All x >= -6

I get

(-inf,-5/2)U[-6,infin) but it doesn't look right

Is this a question?

To find the domain of a function, you need to consider any restrictions on the input variable (x) that would make the function undefined. In this case, the function is f(x) = (sqrt(x+6))/(-2x-5).

One possible restriction is that the denominator (-2x-5) cannot be equal to zero, since division by zero is undefined. To find the value(s) that make the denominator zero, we set -2x-5 = 0 and solve for x.

-2x - 5 = 0
-2x = 5
x = -5/2

So, x = -5/2 is one value of x that makes the denominator zero.

However, we also need to consider the square root term in the numerator. The square root of a negative number is not defined in the real number system. So, the expression inside the square root (x+6) must be non-negative.

x + 6 ? 0
x ? -6

Combining these two conditions, we find that x must be greater than -6 and less than -5/2.

Therefore, the domain of the function is (-6,-5/2).