Question

Consider the following functions.S(x) = x2 - 8x + 16 and g(x) = x - 4Step 2 of 2: Find the domain of()).(x). Express your answer in interval notationAnswerDomain in interval notation:

Answer 1

Question:

Explanation:

Consider the following functions:

$f(x)=x^2\text{ - 8x + 16}$

and

$g(x)=x\text{ - 4}$

then:

$(\frac{f}{g})(x)=\frac{f(x)}{g(x)}=\frac{x^2\text{ -8x +16}}{x\text{ - 4}}$

this is equivalent to:

$(\frac{f}{g})(x)=\frac{x^2\text{ -8x +16}}{x\text{ - 4}}$

now, factoring the numerator we get:

$(\frac{f}{g})(x)=\frac{(x\text{ - 4})(x\text{ -4})}{x\text{ - 4}}$

Simplifying, we get:

$(\frac{f}{g})(x)=\text{ x-4}\frac{}{}$

This is a polynomial, so the domain of this polynomial is all real numbers R. In interval notation, this is:

$(\text{ - }\infty,\text{ }\infty)$

Answer: we can conclude that the correct answer is:

$(\text{ - }\infty,\text{ }\infty)$