2? Missing? ?piece ? ? ? et g?? )? x + 3 a ? nd find a function f that produces the given composition. 4? 2? ? ? ? (?f ° ? )(? ) ? ? x + 6x ? + 20

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 written as f(g(x)), so we can write the following: (f °)(x) = f(g(x)) 2 = f(x + 3) = x + 6x + 20 We cannot apply directly the rule for the square of binomial so we will rearrange this function: (f g)(x) = x + 6x + 20 ° = x + 6x + 9 + 11 2 If we write x and 9 as (x ) and 3 then we can apply the rule for the square of binomial (a + b) = a + 2ab + b : 2 4 2 (f °)(x) = x + 6x + 9 + 11 2 2 2 2 = (x ) + 2 · x · 3 + 3 + 11 2 2 = (x + 3) + 11 Suppose x + 3 = y then f(y) = x + 6x + 9 + 11 = (x + 3) + 11 = y + 11 2 Thus the required function is f(x) = x + 11