Question

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)

Answer 1

(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 2

Part A -
`(f+g)(x)=10x+4`

Part B -
`(f\cdot g)(x)=16x^2-22x-45`

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

Explanation:

Given : Functions
`f(x)=8x+9` and
`g(x)=2x-5`

To find : Complete the function below :

Part A : (f+g)(x)

As
`(f+g)(x)=f(x)+g(x)`

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

`(f+g)(x)=8x+9+(2x-5)`

`(f+g)(x)=8x+9+2x-5`

`(f+g)(x)=10x+4`

Part B : (f ⋅ g)(x)

As
`(f\cdot g)(x)=f(x)\cdot g(x)`

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

`(f\cdot g)(x)=(8x+9)\cdot (2x-5)`

`(f\cdot g)(x)=8x* 2x-8x* 5+9* 2x-9* 5`

`(f\cdot g)(x)=16x^2-40x+18x-45`

`(f\cdot g)(x)=16x^2-22x-45`

Part C : f[g(x)]

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

`f[g(x)]=f[2x-5]`

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

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

`f[g(x)]=16x-31`