jika f(x)=2x²+5x+2 dan g(x)=3x-2. tentukan: a. (fog)(x) b. (gof)(x) c. (fog)(1)

jawab


a)  fog(x)=  f{ g(x)}
= f(3x -2)
= 2(3x-2)² + 5(3x-2) + 2
= 2(9x² - 12x + 4)  + 15x - 10 + 2
= 18 x² -24x + 8 + 15x - 8
= 18 x² - 9x 

b) gof(x) = g {f(x)}
= g(2x² + 5x + 2)
= 2(2x² + 5x + 2) - 2
= 4x² +10x + 4 - 2
= 4x²+ 10x + 2

c)  fog (1) = f { g(1)}
= f (3-2)
= f(1)
= 2+5+2
= 4