Question

Use the functions m(x) = 5x + 4 and n(x) = 6x − 9 to complete the function operations listed below.

Part A: Find (m + n)(x). Show your work.

Part B: Find (m ⋅ n)(x). Show your work.

Part C: Find m[n(x)]. Show your work.

Answer 1

A. (m+n)(x)=
5x+4+6x-9=
11x-5

B. (mn)(x)=
(5x+4)(6x-9)=
30x^2+24x-45x-36=
30x^2-21x-36

C. basically sub n(x) for x in m(x)
m(n(x))=
5(6x-9)+4=
30x-45+4=
30x-41

Answer 2

For this case we have the following functions:

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For the sum of functions we have:

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Substituting values:

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Adding similar terms we have:

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For the multiplication of functions we have:

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Substituting values:

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If we apply the distributive property we have:

`image`

Adding similar terms we have:

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For the composition of functions we have:

`image`

Rewriting we have:

`image`