Answer to Question #186232 in Calculus for Innocent Lorita

Question

Let f(x)=3x-3,g(x)=x+1,h(x)=3x+12. Then (fogohogohogohogoh)(0)=

Answer 1

$h(x)=3x+12\newline g(h(x))=g(3x+12)=3x+13\newline h(g(h(x)))=h(3x+13)=9x+51\newline g(h(g(h(x))))=g(9x+51)=9x+52\newline h(g(h(g(h(x)))))=h(9x+52)=27x+168\newline g(h(g(h(g(h(x))))))=g(27x+168)=27x+169\newline h(g(h(g(h(g(h(x)))))))=h(27x+169)=81x+519\newline g(h(g(h(g(h(g(h(x))))))))=g(81x+519)=81x+520\newline f(g(h(g(h(g(h(g(h(x)))))))))=f(81x+520)=243x+1557\newline \text{put x=0},\newline f(g(h(g(h(g(h(g(h(0)))))))))=1557$