For this case we have that by definition, the domain of a function, is given for all the values for which the function is defined.
We have:
[tex]f (x) = \frac {x + 1} {x ^ 2-6x + 8}[/tex]
The given function is not defined when the denominator is equal to zero. That is to say:
[tex]x ^ 2-6x + 8 = 0[/tex]
To find the roots we factor, we look for two numbers that when multiplied give as a result "8" and when added as a result "-6". These numbers are:
[tex]-4-2 = -6\\-4 * -2 = 8[/tex]
Thus, the factored polynomial is:
[tex](x-4) (x-2) = 0[/tex]
That is to say:
[tex]x_ {1} = 4\\x_ {2} = 2[/tex]
Makes the denominator of the function 0.
Then the domain is given by:
All real numbers, except 2 and 4.
Answer:
x |x≠2,4
