Question

Find(f+g)(x) for the following functions. f(x) = 12x2 + 7x + 2 g(x) = 9x + 7

12x2 + 16x + 2

21x3 + 14x + 2

12x2 + 16x + 9

21x2 + 14x + 2

Answer 1

(f + g)(x) = 12x² + 16x + 9 ⇒ 3rd answer

Explanation:

* Lets explain how to solve the problem

- We can add and subtract two function by adding and subtracting their

like terms

Ex: If f(x) = 2x + 3 and g(x) = 5 - 7x, then

(f + g)(x) = 2x + 3 + 5 - 7x = 8 - 5x

(f - g)(x) = 2x + 3 - (5 - 7x) = 2x + 3 - 5 + 7x = 9x - 2

* Lets solve the problem

∵ f(x) = 12x² + 7x + 2

∵ g(x) = 9x + 7

- To find (f + g)(x) add their like terms

∴ (f + g)(x) = (12x² + 7x + 2) + (9x + 7)

∵ 7x and 9x are like terms

∵ 2 and 7 are like terms

∴ (f + g)(x) = 12x² + (7x + 9x) + (2 + 7)

∴ (f + g)(x) = 12x² + 16x + 9

* (f + g)(x) = 12x² + 16x + 9

Answer 2

For this case we have the following functions:

`f (x) = 12x ^ 2 + 7x + 2\\g (x) = 9x + 7`

We must find
`(f + g) (x).`

By definition we have to:

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

So:

`(f + g) (x) = 12x ^ 2 + 7x + 2 + (9x + 7)\\(f + g) (x) = 12x ^ 2 + 7x + 2 + 9x + 7`

We add similar terms:

`(f + g) (x) = 12x ^ 2 + 7x + 9x + 2 + 7\\(f + g) (x) = 12x ^ 2 + 16x + 9`

Answer:

Option C