1. ## Find Function g

Given f(x) = 3x + 1 and (f + g)(x) = 6 - (x/2), find the function g.

I know that (f + g)(x) = f(x) + g(x).

My Set up:

f(x) + f(x) + g(x)

3x + 1 + 6 - (x/2)

I must then simplify.

Correct thus far?

2. ## Re: Find Function g

Originally Posted by harpazo
Given f(x) = 3x + 1 and (f + g)(x) = 6 - (x/2), find the function g.

Correct thus far?
no. In fact I have no idea what you are doing.

$g(x) = (f+g)(x) - f(x)$

$g(x) = \left(6-\dfrac x 2\right) - (3x+1)$

now simplify

3. ## Re: Find Function g

Originally Posted by romsek
no. In fact I have no idea what you are doing.

$g(x) = (f+g)(x) - f(x)$

$g(x) = \left(6-\dfrac x 2\right) - (3x+1)$

now simplify
I never saw a problem like this before. Thanks. I will work on it.

4. ## Re: Find Function g

g(x) = 6 - x/2 - (3x + 1)

g(x) = (12 - x)/2 - (3x + 1)/1

g(x) = (12 - x -2(3x + 1)/2

g(x) = (12 - x - 6x - 2)/2

g(x) = (10 - 7x)/2

g(x) = 5 - (7x/2)

Correct?

5. ## Re: Find Function g

Originally Posted by harpazo
g(x) = 6 - x/2 - (3x + 1)

g(x) = (12 - x)/2 - (3x + 1)/1

g(x) = (12 - x -2(3x + 1)/2

g(x) = (12 - x - 6x - 2)/2

g(x) = (10 - 7x)/2

g(x) = 5 - (7x/2)

Correct?
using this function does $(f+g)(x) = 6 - \dfrac x 2$ ?

You need to learn to be able to check your own work, and I don't want to hear about your limited time.

6. ## Re: Find Function g

f(x) + g(x)

3x + 1 + 5 - (7x/2)

6 + 3x - (7x/2)

6 + (3x/1) - (7x/2)

6 + (6x - 7x)/2

6 - (x/2)

It proves to be correct.

So, g(x) = 5 - (7x/2) is the correct answer.