Find the domain of the function.
f(x)=(sqrt x+6)/(-2x-5)
Write your answer as an interval or union of intervals.
(-6,-5/2)and(-5/2,infinity)
the simplest way to describe the domain:
x ? -6 , x ? -5/2
I'm lost
To find the domain of the function f(x), we need to determine all possible values of x for which the function is defined.
In this case, there are two conditions that need to be satisfied for the function to be defined:
1. The denominator (-2x - 5) should not be equal to zero since division by zero is undefined.
2. The expression inside the square root (√x + 6) should not involve taking the square root of a negative number.
First, let's consider the denominator:
-2x - 5 ≠ 0
Solving this inequality gives us:
-2x ≠ 5
x ≠ -5/2
So, the function is not defined when x = -5/2.
Next, let's consider the expression inside the square root:
√x + 6 ≥ 0
The square root of any non-negative real number is defined. Therefore, we don't have any restrictions on the expression inside the square root.
Now, combining both conditions, the resulting domain for the function f(x) is:
(-∞, -5/2) ∪ (-5/2, ∞)
So, the domain of the function f(x) is the interval (-∞, -5/2) union (-5/2, ∞).