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Natalka [10]
3 years ago
14

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

Mathematics
1 answer:
Ostrovityanka [42]3 years ago
7 0

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

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