Let $f(x)$ be the polynomial \[f(x)=x^7-3x^3+2.\]If $g(x) = f(x + 1)$, what is the sum of the coefficients of $g(x)$?

\(g(x) = f(x+1) = (x+1)^7 - 3(x+1)^3 + 2\)

Now this is some polynomial

\(g(x) = \sum \limits_{k=0}^7~c_k x^k \\ \text{and we can find the sum of the coefficients by simply finding }g(1)\)

\(g(1) = 2^7 - 3(2^3)+2 = 128 - 24+2 = 106\)