Write the resulting function if the transformation f(x+3)+9 is applied on the function f(x)=x^2+1 a) x^2+13 b)x^2+19 c)x^2+6x+19 d)x^2+3x+13

We have the following function:
 f (x) = x ^ 2 + 1
 We apply the transformation f (x + 3) +9:
 g (x) = (x + 3) ^ 2 + 1 + 9
 Rewriting we have:
 g (x) = (x + 3) * (x + 3) + 1 + 9
 g (x) = (x ^ 2 + 3x + 3x + 9) + 1 + 9
 g (x) = (x ^ 2 + 6x + 9) + 1 + 9
 g (x) = x ^ 2 + 6x + 9 + 1 + 9
 g (x) = x ^ 2 + 6x + 19
 
 the resulting function if the transformation f (x + 3) +9 is applied on the function f (x) = x ^ 2 + 1 is:
 c) x ^ 2 + 6x + 19

Main idea on left, details on right