Question

Va rog mult !!!
Se dau functiile f,g:R-R,f(x)=3-2x,g(x)=3x+1. Sa se calculeze: (fog)(x)-(gof)(x),x apartine R

Answer 1

(f○g)(x) = f(g(x)) = 3-2g(x) = 3-2(3x+1) = 3-6x-2 = 1-6x

(g○f)(x) = g(f(x)) = 3f(x)+1 = 3(3-2x)+1 = 9-6x+1 = 10-6x

=> (f○g)(x) - (g○f)(x) = 1-6x - (10-6x) = 1-6x-10+6x = -9