Question

If f(x + 1) = x² - 1 and g(x + 1) = x² + 1, find f(x) + g(x).

Answer 1

If
`f(x+1) = x^2 - 1`, then

`f(x) = f((x - 1) + 1) = (x - 1)^2 - 1`

Similarly,

`g(x + 1) = x^2 + 1 \implies g(x) = g((x-1) + 1) = (x-1)^2 + 1`.

Then

`f(x) + g(x) = \bigg((x-1)^2 - 1\bigg) + \bigg((x-1)^2 + 1\bigg) = \boxed{2(x-1)^2}`