Question 273851
Since {{{(f+g)(x)=10-3x}}}, this means that {{{f(x)+g(x)=10-3x}}}. Solve for 'f(x)' to get {{{f(x)=10-3x-g(x)}}}



Also, because {{{(f-g)(x)=5x-14}}}, we know that {{{f(x)-g(x)=5x-14}}}



Now plug {{{f(x)=10-3x-g(x)}}} into {{{f(x)-g(x)=5x-14}}} to get {{{10-3x-g(x)-g(x)=5x-14}}}



Combine like terms to get {{{10-3x-2g(x)=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).