Vivian L. answered • 10/16/13

Microsoft Word/Excel/Outlook, essay composition, math; I LOVE TO TEACH

Hi Paige;

1.) f(x)=(x

^{2}-4x+3)/(x-1)At first sight, we might guess that the domain is...

(-infinity,1)U(1, +infinity)

1 must be excluded because it would render (x-1) as zero.

However, the denominator can be factored with one of the parenthetical equations as (x-1)...

f(x)=[(x-3)(x-1)]/(x-1)

Let's verify (x-3)(x-1) with FOIL...

FIRST...x

^{2}OUTER...-1x

INNER...-3x

LAST...+3

x

^{2}-x-3x+3x

^{2}-4x+3f(x)=[(x-3)(x-1)]/(x-1)

Let's cancel...

f(x)=[(x-3)(x-1)]/(x-1)

f(x)=x-3

The domain is infinity.

2.) g(x)=(x

^{2}-4)(x-3)/(x^{2}-x-6)Let's factor (x

^{2}-x-6)...Is one of the parenthetical equations (x-3)?

(x-3)(x+2)

Let's FOIL...

FIRST...x

^{2}OUTER...2x

INNER...-3x

LAST...-6

x

^{2}+2x-3x-6x

^{2}-x+6(x

^{2}-4)(x-3)/(x-3)(x+2)Let's cancel where appropriate...

(x

^{2}-4)(x-3)/(x-3)(x+2)(x

^{2}-4)/(x+2)Initially, it would seem that the domain is infinity excluding -2 such that the numerator can render 0. However, it would seem that the current denominator can also be factored to include (x+2)...

(x+2)(x-2)/(x+2)

FIRST...x

^{2}OUTER...-2x

INNER...2x

LAST...-4

Let's cancel where appropriate...

(x+2)(x-2)/(x+2)

x-2

There are no limitations on the domain. It is from negative infinity to positive infinity.

3.) F(x)=(x

^{3}-2x^{2})/(x-2)Can the denominator be factored to include (x-2)?

x

^{3}-2x^{2}x(x

^{2}-2x)x(x-2)(x+2)

[x(x-2)(x+2)]/(x-2)

Let's cancel where appropriate...

[x(x-2)(x+2)]/(x-2)

There are no limitations on the domain.

4.) G(x)=√(x-1)

We already know that a negative number cannot be square rooted. Therefore, let's begin with the one number which would set the limit...

(x-1)?0

x?1

The domain is (1, +infinity)

5.) f(x)=3/√(x-4)

This equation cannot be factored.

We already know that the domain cannot include 4 because that would render the numerator as 0.

We already know that a negative number cannot be square rooted. Therefore, let's begin with the one number which would set the limit...

(x-4)?0

x?4

The domain is (4, +infinity).

Vivian L.

Paige;

How are you doing? I am very curious as to how you scored. Please e-mail me and let me know.

It was always my understanding that the way to establish domain is by reducing the equation to its simplest form, and then finding limitations.

I was on another website, executing some research. According to this, the original equation is used to set the limits.

What did your instructor say?

Report

10/20/13

Paige N.

Good Day Madam,

My instructor haven't said anything yet as of now. He gave us this as an assignment and it is due tomorrow. I tried to ask help from my cousin who is also good at math, and he said that my answers starting from 1 to 3 are quite different from what he expected,
but rest assured that your answers from 4 to 5 are correct. :) For example, he said that the answer for number 1 is "all real numbers except 1" for number 2 he said that the domain is "all real numbers except -2 and 3" while for number 3 he said that the domain
is "all real numbers except 2". But I really appreciate your hardwork for answering this! :) Please do comment if you have any ideas too :)

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10/21/13

Paige N.

10/16/13