Chenrengelca
Answered

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 :

apologiabiology
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
carlosego

For this case we have the following functions:

[tex] m (x) = 5x + 4

n (x) = 6x - 9
[/tex]


For the sum of functions we have:

[tex] (m + n) (x) = m (x) + n (x)
[/tex]

Substituting values:

[tex] (m + n) (x) = (5x + 4) + (6x - 9)
[/tex]

Adding similar terms we have:

[tex] (m + n) (x) = 11x - 5
[/tex]


For the multiplication of functions we have:

[tex] (m ⋅ n) (x) = m (x) * n (x)
[/tex]

Substituting values:

[tex] (m + n) (x) = (5x + 4) * (6x - 9)
[/tex]

If we apply the distributive property we have:

[tex] (m + n) (x) = 30x ^ 2 - 45x + 24x - 36
[/tex]

Adding similar terms we have:

[tex] (m + n) (x) = 30x ^ 2 - 21x - 36
[/tex]


For the composition of functions we have:

[tex] m [n (x)] = 5 (6x - 9) + 4
[/tex]

Rewriting we have:

[tex] m [n (x)] = 30x - 45 + 4

m [n (x)] = 30x - 41 [/tex]

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