What is the domain of the function f(x) = x+1 / x2-6x+8

Question

asked Dec 23, 2020 16.8k views

2 Answers

Adam Houldsworth · Answer 1 · 2020-12-29T21:09:56+0000

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:

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

The given function is not defined when the denominator is equal to zero. That is to say:

x ^ 2-6x + 8 = 0

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:

$-4-2 = -6\\-4 * -2 = 8$

Thus, the factored polynomial is:

(x-4) (x-2) = 0

That is to say:

$x_ {1} = 4\\x_ {2} = 2$

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