QuestionDetermine the domain of the function $f(x)=\frac{x-8}{x+8}$ in interval notation.

Studdy Solution

STEP 1

Assumptions1. The function is given by $f(x)=\frac{x-8}{x+8}$ . We are to find the domain of the function3. The domain of a function is the set of all possible input values (x-values) which will output real numbers

STEP 2

The denominator of a fraction cannot be zero because division by zero is undefined in mathematics. Therefore, we need to find the values of $x$ that would make the denominator of the function $f(x)$ zero.
$x+8 =0$

STEP 3

olving the equation $x+8 =0$ for $x$ gives us $x = -8$

STEP 4

So, $x = -8$ is the value that would make the denominator of the function $f(x)$ zero. Therefore, this value is not included in the domain of the function.

STEP 5

The domain of the function $f(x)$ is all real numbers except $x = -8$ . In interval notation, this is written as $(-\infty, -8) \cup (-8, \infty)$ The domain of $f(x)=\frac{x-8}{x+8}$ is $(-\infty, -8) \cup (-8, \infty)$ .

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