g(x) = x^2 - 11x + 30

g(f(x)) = x^2 - 8x^3 + 11x^2 + 20x + 6

Let g and f be the monic polynomial functions that satisfy the system above. What is the value of f(7)?

Can you check your input please.

You have x^2 twice in the second function.

g(f(x)) = x^4 - 8x^3 + 11x^2 + 20x + 6

Let f(x)= x^2 +Bx+C

then

g(f(x))= (x^2 +Bx+C)^2 - 11(x^2 +Bx+C) +30

Now just expeand it and equate the coefficients for find B and C ,

It is not that difficult.