I can’t seem to solve (fogof)(x) given f(x)= -3x^2+1 and g(x)=5/x-4

Question

I know how to do (fog)(x) but this next level is tough and my teacher makes it sound confusing

Answer 1

Just do it again. f(g(f(x)))

f(x)=-3x²+1

g(f(x)) = 5 / (-3x²+1)-4 = - (5)/(3x²+3)

f(g(f(x)) = -3(- (5)/(3x²+3))² + 1 = -75 / (3x²+3)² + 1 = -75 / (9x^4+18x²+9) + 1 ■