For all values of x, f(x) = (x + 1)^2 and g(x) = 2(x-1). Show that gf(x) = 2x(x + 2) and find g^-1(7)
gf(x) means you are applying the function f to x (giving you f(x)) and then you are applying the function g to f(x). Since g(x) = 2(x-1), g(f(x)) =2(f(x)-1). This means after substitution, gf(x) = 2((x+1)2 -1), expanding and simplifying this gives the answer.g-1( x) is the inverse function of g(x). Lets call g(y) = x, hence x = 2(y-1), rearrange this to make y the subject. This will give you y = (x + 2)/2. let y = g-1(x), hence g-1(x) = (x + 2)/2. Now we substitute x = 7 and get the answer 9/2.
AP
