2? Missing? ?piece ? ? ? et g?? )? x + 3 a ? nd find a function f that produces the given composition. 4? 2? ? ? ? ? ° g?? )? ) ? ? x + 6?x + 9

Step-by-step solution Step 1 of 3 Step 2 of 3 The function (f g°(x)is the composite function and it can be writt en as f(g(x)), so we can write the following: (f °)(x) = f(g(x)) = f(x +3) 4 2 = x +6x +9 4 2 2 2 We will write x and 9 as (x ) and 3 . If we use the rule for the square of binomial 2 2 2 (a+b) = a +2ab+b then we have: 2 (f °)(x) = x +6x +9 2 = (x ) +2·x ·3+3 2 2 = (x +3) Suppose x +3 = y then 2 f(y) = x +6x +9 2 2 = (x +3) 2 = y 2 Thus the required function is f(x) = x