what is the domain of the function $f(x)=\frac{x + 1}{x^{2}-6x + 8}$?\no all real numbers\no all real…

Answer:

D. all real numbers except 2 and 4

Explanation:

Step1: Identify non - zero denominator condition

The denominator of the function $f(x)=\frac{x + 1}{x^{2}-6x + 8}$ cannot be zero. So we set $x^{2}-6x + 8\neq0$.

Step2: Factor the quadratic equation

Factor $x^{2}-6x + 8$ as $(x - 2)(x - 4)\neq0$.

Step3: Solve for x

If $(x - 2)(x - 4)=0$, then $x=2$ or $x = 4$ by the zero - product property. So the domain is all real numbers except $x = 2$ and $x=4$.