Question

Drag the tiles to the correct boxes to complete the palrs.

If f(x) = 2x+3 and g(x) = x -1, find the values of combining these functions. Match each combined function to its corresponding value.

(f+g)(2)
(f-g)(4)
(f ÷g)(2)
(f x g)(1)

-4
7/3
10
0​

Answer 1

(f+g)(2) = 4

(f-g)(4) = 8

(f ÷g)(2) = 7

(f x g)(1) = 0

Explanation:

We are given these following functions:

`f(x) = 2x + 3`

`g(x) = x - 1`

(f+g)(2)

`(f+g)(x) = f(x) + g(x) = 2x + 3 + x - 1 = 3x - 2`

At
`x = 2`

`(f+g)(2) = 3(2) - 2 = 6 - 2 = 4`

Then

(f+g)(2) = 4

(f-g)(4)

`(f-g)(x) = f(x) - g(x) = 2x + 3 - (x - 1) = 2x + 3 - x + 1 = x + 4`

At x = 4

`(f-g)(4) = 4 + 4 = 8`

Then

(f-g)(4) = 8

(f ÷g)(2)

`(f / g)(x) = (f(x))/(g(x)) = (2x+3)/(x-1)`

At x = 2

`(f / g)(2) = (7)/(1) = 7`

Then

(f ÷g)(2) = 7

(f x g)(1)

`(f * g)(x) = f(x)g(x) = (2x+3)(x-1) = 2x^2 -2x + 3x - 3 = 2x^2 + x - 3`

Then

`(f * g)(1) = 2(1)^2 + 1 - 3 = 3 + 1 - 3 = 0`

So

(f x g)(1) = 0