Missing? ?piece? ?Let g?(?x?)?= x? + 3 ?and find a function f that produces the given composition. (?g? °? ?? ?) ?= x?3?+3

Step-by-step solution Step 1 of 3 Step 2 of 3 The function (g f)(°)is the composite function and it can be written as g(f(x)), so we can write the following: (g f)(x) = g(f(x)) ° g(x) = x +3 2 g(f(x)) = f(x) +3…….(1) 2 From the text of the problem we have (g ° f)(x) = g(f(x)) = x +3, therefore based on the relation (1) we can write the following: f(x) +3 = x +3 3 Let’s rearrange this relation: 2 2 f(x) +3 = x +3 3 2 2 f(x) = x +333 2 2 f(x) = x 3 a b ab We will use the rule (x ) = x : 2 1 2 f(x) = (x ) 3 1 f(x) = x 3