Question

f,g:R=R,f(x)=2x-1,g,g(x)=3x-4 calculați dog, gof, fof, gog​

Answer 1

f(x) = 2x-1

g(x) = 3x - 4

○ (f○g)(x) = f( g(x) ) = 2 · g(x) - 1 = 2 · (3x-4) - 1 = 6x - 8 - 1 = 6x -9

○ (g○f)(x) = g( f(x) ) = 3 · f(x) - 4 = 3 · (2x-1) - 4 = 6x - 3 - 4 = 6x - 7

○ (f○f)(x) = f( f(x) ) = 2 · f(x) - 1 = 2 (2x-1) - 1 = 4x - 2-1 = 4x-3

○ (g○g)(x) = g( g(x) ) = 3· g(x) - 4 = 3(3x-4) - 4 = 9x - 12 - 4 = 9x - 16