combination and composition 8

Question

Algebraically show that each of the given combinations are equivalent to the given functions.  is equivalent to  given: ;  ; 



 

 

 

 

 

Answer 1

Hi Stephanie. This question asks you to show h(x) • j(x) = k(x).

Start by writing out what h(x) • j(x) is in terms of the variable x.

h(x) • j(x) = (-3x-1)(-7x+11)

To solve this, you will need to multiply these polynomials by the FOIL method. If you are unfamiliar with FOIL, it stands for First Outer Inner Last. You will multiply the first terms with each other. Then you will multiply the outer terms, then the inner terms, and then the last terms. Lastly, you will add these four products together to get the answer.

Following the FOIL method, the first terms are multiplied together. In this case, the product of the first terms is

-3x • -7x = 21x²

The outer terms are multiplied together.

-3x • 11 = -33x

The inner terms are multiplied together.

-1 • -7x = 7x

The last terms are multiplied together.

-1 • 11 = -11

Now you will add all these products from the FOIL method together

(-3x-1)(-7x+11) = 21x² - 33x + 7x - 11

(-3x-1)(-7x+11) = 21x² - 26x - 11

Because 21x² - 26x - 11 is equal to k(x), you have just shown that h(x) • j(x) = k(x).

Answer 2

h(x)=−3x−1 ; j(x)=−7x+11

Multiply by FOIL

(−3x−1)(−7x+11)

First: (-3x)(-21x) = 21x²

Outer: (-3x)(11) = -33x

Inner: (-1)(-7x)=7x

Last: (-1)(11) = -11

21x²-33x+7x-11 Combine like terms

21x²−26x−11