Question

What is the domain of the functionf(x)=x+1/x^2-6x+8 ? all real numbers all real numbers except –1 all real numbers except –4 and –2 all real numbers except 2 and 4

Answer 1

Answer: The correct option is 4. The domain of f(x) is all real numbers except 2 and 4.

Explanation:

The given function is,

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

Use factoring by grouping method to factorize the domain.

$f(x)=\frac{x+1}{x^2-4x-2x+8}$

$f(x)=\frac{x+1}{x(x-4)-2(x-4)}$

$f(x)=\frac{x+1}{(x-4)(x-2)}$

The domain of a rational function is the intersection of domain of numerator or denominator expect those value for which the denominator function is 0.

The domain of numerator function (x+1) is all real number. The domain of denominator function (x-4)(x-2) is all real number.

The value of denominator equal to 0 when the value of x is 2 or 4. So the function f(x) is not defined for x=2 and x=4.

Therefore the domain of f(x) is all real numbers except 2 and 4. The fourth option is correct.

Answer 2

I assume you mean f(x) = (x+1) / (x^2 - 6x + 8)

Then f(x) = (x+1)/ (x-2)(x-4)

So the domain will be all real numbers except 2 and 4