Question

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

Answer 1

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

Explanation:

We are given the following function:

`f(x) = (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) = (-(-6) + √(4))/(2) = 4`

`x_(2) = (-(-6) - √(4))/(2) = 2`

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