If [tex]f(x+1) = x^2 - 1[/tex], then
[tex]f(x) = f((x - 1) + 1) = (x - 1)^2 - 1[/tex]
Similarly,
[tex]g(x + 1) = x^2 + 1 \implies g(x) = g((x-1) + 1) = (x-1)^2 + 1[/tex].
Then
[tex]f(x) + g(x) = \bigg((x-1)^2 - 1\bigg) + \bigg((x-1)^2 + 1\bigg) = \boxed{2(x-1)^2}[/tex]
