Given the f(x)=x^2+3x, determine h(1) where h(x)=f^2(x+1)

Question

Can you please explain the steps to solve this problem if possible?

Answer 1

f^2(x) =  [x^2 + 3x]^2 

 

       = x^4 + 6x^3 + 9x^2

 

 

h(X) = f^2(x+1) =  (x+1)^4 + 6(x+1)^3 + 9(x+1)^2

 

      =  (x+1)^2  [(x+1)^2 + 6(x+1) + 9]

 

     = (x+1)^2 [  (x+1)+3]^2

 

   = (x+1)^2 [ x+4]^2

 

h(1) = (1+1)^2 * (1+4)^2

       = 2^2 * 5^2

      = 4*25

      = 100