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Use the functions f(x) = 8x + 9 and g(x) = 2x − 5 to complete the function operations listed below.

Part A: Find (f + g)(x). Show your work. (3 points)

Part B: Find (f ⋅ g)(x). Show your work. (3 points)

Part C: Find f[g(x)]. Show your work. (4 points)

Respuesta :

Aishani
(a)f(x) + g(x) = 8x + 9 + 2x - 5 = 10x + 4

(b)(f.g)(x) = (8x + 9) (2x - 5)
= 16x - 40 + 18x - 45
= 34x - 85

(c)f(g(x)) = 8(2x - 5) + 9
= 16x - 40 + 9
= 16x - 31

Hope it helped!

Answer:

Part A - [tex](f+g)(x)=10x+4[/tex]

Part B - [tex](f\cdot g)(x)=16x^2-22x-45[/tex]

Part C - [tex]f[g(x)]=16x-31[/tex]

Step-by-step explanation:

Given : Functions  [tex]f(x)=8x+9[/tex] and [tex]g(x)=2x-5[/tex]

To find : Complete the function below :

Part A : (f+g)(x)

As [tex](f+g)(x)=f(x)+g(x)[/tex]

Substitute the value of f(x) and g(x)

[tex](f+g)(x)=8x+9+(2x-5)[/tex]

[tex](f+g)(x)=8x+9+2x-5[/tex]

[tex](f+g)(x)=10x+4[/tex]

Part B : (f ⋅ g)(x)

As [tex](f\cdot g)(x)=f(x)\cdot g(x)[/tex]

Substitute the value of f(x) and g(x)

[tex](f\cdot g)(x)=(8x+9)\cdot (2x-5)[/tex]

[tex](f\cdot g)(x)=8x\times 2x-8x\times 5+9\times 2x-9\times 5[/tex]

[tex](f\cdot g)(x)=16x^2-40x+18x-45[/tex]

[tex](f\cdot g)(x)=16x^2-22x-45[/tex]

Part C : f[g(x)]

f[g(x)] means substitute value of g(x) in place of x in f(x)

[tex]f[g(x)]=f[2x-5][/tex]

[tex]f[g(x)]=8(2x-5)+9[/tex]

[tex]f[g(x)]=16x-40+9[/tex]

[tex]f[g(x)]=16x-31[/tex]

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