SOLUTION: I am completely stumped on this question. Given (f+g)(x)=10-3x and (f-g)(x)=5x-14, find f(x) and g(x). Thanks so much.

Algebra ->  Functions -> SOLUTION: I am completely stumped on this question. Given (f+g)(x)=10-3x and (f-g)(x)=5x-14, find f(x) and g(x). Thanks so much.      Log On


   

Question 273851: I am completely stumped on this question.
Given (f+g)(x)=10-3x and (f-g)(x)=5x-14, find f(x) and g(x).
Thanks so much.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since %28f%2Bg%29%28x%29=10-3x, this means that f%28x%29%2Bg%28x%29=10-3x. Solve for 'f(x)' to get f%28x%29=10-3x-g%28x%29


Also, because %28f-g%29%28x%29=5x-14, we know that f%28x%29-g%28x%29=5x-14


Now plug f%28x%29=10-3x-g%28x%29 into f%28x%29-g%28x%29=5x-14 to get 10-3x-g%28x%29-g%28x%29=5x-14


Combine like terms to get 10-3x-2g%28x%29=5x-14


From here, simply solve for 'g(x)' (think of g(x) as any other variable). Once you have g(x), use that to find f(x).