The function $$ g $$ is defined below. $$ g(x)=\frac{x-3}{x^{2}-6 x+9} $$ Find all values of $$ x $$ that are NOT in the domain of $$ g $$. If there is more than one value, separate them with commas.

Question

UpStudy AI · Accepted Answer

The value of $$ x $$ not in the domain of $$ g $$ is 3. To find the values of $$ x $$ that are not in the domain of the function $$ g(x) = \frac{x-3}{x^2 - 6x + 9} $$, we need to determine when the denominator is equal to zero, since division by zero is undefined. First, we simplify the denominator: $$ x^2 - 6x + 9 $$ This expression can be factored. We notice that it is a perfect square: $$ x^2 - 6x + 9 = (x - 3)^2 $$ Now, we set the denominator equal to zero to find the values of $$ x $$ that are not in the domain: $$ (x - 3)^2 = 0 $$ Taking the square root of both sides, we find: $$ x - 3 = 0 $$ Solving for $$ x $$, we get: $$ x = 3 $$ Thus, the only value of $$ x $$ that is not in the domain of $$ g $$ is: $$ \boxed{3} $$

The function \( g \) is defined below. \[ g(x)=\frac{x-3}{x^{2}-6 x+9} \] Find all values of \( x \) that are NOT in the domain of \( g \). If there is more than one value, separate them with commas.

UpStudy ThothAI Solution

Step-by-step Solution

Quick Answer

The function \( g \) is defined below. \[ g(x)=\frac{x-3}{x^{2}-6 x+9} \] Find all values of \( x \) that are NOT in the domain of \( g \). If there is more than one value, separate them with commas.

UpStudy ThothAI Solution

Step-by-step Solution

Quick Answer

Related Questions