f(x) = (x+1)^2 and g(x) = 2(x-1); Show that gf(x) =2x(x+2)

In this question, we are being asked to combine the functions f(x) and g(x). The function gf(x) is 'putting in' the function f(x) into g(x). What we do is substitute whatever f(x) is into the g function like so:gf(x) = g(f(x)) = g ((x+1)^2) = 2 ((x+1)^2 - 1) = 2((x^2 + 2x + 1) - 1) = 2 (x^2 +2x)We can then factor out the x to get 2x(x+2), which is what we were asked to prove.