Question

Use the functions a(x) = 3x + 10 and b(x) = 5x − 6 to complete the function operations listed below.

Part A: Find (a + b). Show your work.

Part B: Find (a - b). Show your work.

Part C: Find (a * b). Show your work.

Answer 1

Part A

The functions a(x) = 3x + 10 and b(x) = 5x − 6 to complete the function operations listed below.

(a+b)(x)=a(x)+b(x)

(a+b)(x)=(3x+10)+(5x-6)

(a+b)(x)=3x+5x+10-6

(a+b)(x)=8x+4

Part B.

(a-b)(x)=a(x)-b(x)

(a-b)(x)=(3x+10)-(5x-6)

Expand the parenthesis to get:

(a-b)(x)=3x+10-5x+6

(a-b)(x)=3x-5x+10+6

(a-b)(x)=-2x+16

Part C

(a*b)(x)=a(x)*b(x)

(a*b)(x)=(3x+10)*(5x-6)

We expand to get:

`a * b = 15 {x}^(2) - 18x + 50x - 60`

`a * b = 15 {x}^(2) + 32x - 60`

Answer 2

(a + b) = 8x +4

(a - b) = -2x +16

(a * b) =
`15x^(2)+32x-60`

Explanation:

We have been given the functions;

a(x) = 3x + 10 and b(x) = 5x − 6

Part A:

(a + b) = a(x) + b(x) # we simply add the two given functions

(a + b) = 3x + 10 + 5x − 6

(a + b) = 8x + 4

Part B:

(a - b) = a(x) - b(x) # we simply subtract the two given functions

(a - b) = (3x + 10 ) - (5x − 6)

(a - b) = 3x + 10 -5x +6

(a - b) = -2x + 16

Part C:

(a * b) = a(x)*b(x)

# we simply find the product of the two given functions

(a * b) = (3x + 10)*(5x − 6)

(a * b) =
`15x^(2)-18x+50x-60=15x^(2)+32x-60`