Composition and Inverse - Assignment Example

Composition and Inverse College Composition and Inverse We define the following functions:f(x) = 2x + 5 g(x) = x2 - 3 h(x) = (7-x)/3                    Compute (f – h)(4).  To evaluate (f – h)(4), the function (f – h)(x) may be found first by subtracting the function h(x) from the function f(x). So, f(x) – h(x) = 2x + 5 – --- f(x) – h(x) = --- (f – h)(x) = Then upon substitution of 4 into ‘x’, (f – h) (4) = = 12Evaluate the following two compositions:A: (fog)(x) would pertain to a composition where the function g(x) is composed within the function f(x) such that g(x) serves as an expression that replaces ‘x’ in f(x) as follows --- () (x) = 2 () + 5 = 2x2 – 6 + 5 so the expression x2 – 3 takes the place of ‘x’ in 2x + 5, then applying distributive property and combining like terms, that reduces to --- () (x) = 2x2 – 1 B: (hog)(x) would pertain to a composition where the function g(x) is composed within the function h(x), and in a similar function (as in part A), g(x) serves as an expression that replaces ‘x’ herein – --- () (x) = = so the expression x2 – 3 takes the place of ‘x’ in (7 – x)/3, then distributing the negative sign into the quantity to remove the parentheses and combining like terms, that simplifies to – --- () (x) = Graph the g(x) function and transform it so that the graph is moved 6 units to the right and 7 units down.

 On transforming g(x) so that the graph shitfs 6 units to the right and 7 units down, the new function would g(x) = - 3 - 7 or - 10 whose graph looks –2. Find the inverse functions:C:   (x) --- from y = 2x + 5, variables may be switched so that x = 2y + 5, then isolating the ‘y’, 5 must be subtracted (both sides) to have x – 5 = 2y, whereupon division by 2, --- (x) = D:  (x) --- from y = (7 – x)/3, switching of variables yields 3x = 7 – y, then adding ‘y’ on both sides of the equation and subtracting ‘3x’ to get ‘y’ by itself on one side, --- (x) = 7 – 3x