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:

Step-by-step explanation:

Consider the following functions:

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

and

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

then:

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

this is equivalent to:

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

now, factoring the numerator we get:

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

Simplifying, we get:

`((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)`