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
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.