Question

What is the domain of the function f(x) =x+1/ X^2-6x+8?

Answer 1

Answer:

The domain of the function is all real values of x, except $x = 4$ and $x = 2$

Step-by-step explanation:

We are given the following function:

$f(x) = \frac{x+1}{x^2-6x+8}$

It's a fraction, so the domain is all the real values except those in which the denominator is 0.

Denominator:

Quadratic equation with $a = 1, b = -6, c = 8$

Using bhaskara, the denominator is 0 for these following values of x:

$\Delta = (-6)^2 - 4(1)(8) = 36-32 = 4$

$x_{1} = \frac{-(-6) + \sqrt{4}}{2} = 4$

$x_{2} = \frac{-(-6) - \sqrt{4}}{2} = 2$

The domain of the function is all real values of x, except $x = 4$ and $x = 2$