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?
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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
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.
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?
Last edited by harpazo; Dec 2nd 2018 at 07:46 PM.
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.
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.