# Compositions and Inverses Essay

690 WordsMay 7, 20133 Pages
Composition and Inverse Jack Lewis Mat 222 Instructor: Dr. Dariush Azimi January 14, 2013 Composition and Inverse The assignment paper for this week is to define the following functions of Elementary and Intermediate Algebra: Problem number 1) fx=2x+5, Problem number 2) gx=x2- 3, and Problem number 3) hx= 7-x3. Compute (f – h)(4). Evaluate the following two compositions: and . Transform the g(x) function so that the graph is moved 6 units to the right and 7 units down. Find the inverse functions and . 1. Write a two to three page paper that is formatted in APA style and according to the Math Writing Guide. Format your math work as shown in the example and be concise in your reasoning. In the body of your essay,…show more content…
= 5(x2 + 2) – 3 The rule of f is applied to g. = 5x2 + 10 - 3 Simplifying. (f g)(x) = 5x2 + 7 The final results Now we will compose the following: (h g)(x) = h(g(x)) The rule of h will work on g. = h(x2 – 3) = 3 + (x2 + 2) The rule of h is applied to g. 7 (h g)(x) = 5 + x2 The final results. 7 Next we are asked to transform g(x) so that the graph is placed 6 units to the right and 7 units downward from where it would be right now. Six units to the right means to put -6 in with x to be squared. Seven units downward means to put -7 outside of the squaring. The new function will look like this: G(x) = (x – 6)2 + 2 – 7 G(x) = (x – 6)2 – 5 Our last job is to find the inverse of two of our functions, f and h. To find the inverse we will write the function with y instead of the function name, then we will switch the places of x and y, and solve for y again. Here are the functions: f(x) = 5x – 3 h(x) = 3 + x 7 Here we replace f(x) and h(x) with y: y = 5x – 3 y = 3 + x 7 Here we switch the y and the x: x = 5y – 3 x = 3 + y 7 Now we solve for y: Add 3 to both sides. Multiply both sides by 7. x + 3 = 5y 7x = 3 + y One more solving step: Divide both sides by 5. Subtract 3 from both sides.. x + 3 = y 7x – 3 = y 5 y = x + 3 y = 7x – 3 5 Presenting the inverse functions: f -1(x) = x + 3 h-1(x) = 7x – 3 5 Thus we have evaluated, combined, composed, and found inverses of our