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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)?

 May 30, 2022
 #1
avatar+117494 
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Can you check your input please.

You have x^2 twice in the second function.

 May 30, 2022
 #2
avatar+117494 
+1

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

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.

 May 30, 2022

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