MAT 222 Compostition and Inverse

May 12th, 2015
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Composition and Inverse Read the following instructions to complete this assignment: We define the following functions: f(x)=2x+5 g(x)= x^2-3 h(x)=(7-x)/3 Compute (f – h)(4). Evaluate the following two compositions: A: (f o g) (x) B: (h o g) (x) Graph the g(x) function and transform it so that the graph is moved 6 units to the right and 7 units down. Find the inverse functions: C: f -1 (x) D: h-1 (x) Write a two- to three-page paper (not including the title page) 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, do the following: Demonstrate your solution to the above problems, making sure to include all mathematical work as well as explanations for each step.

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Composition and InverseComposition of two functionsComposition of two functions means putting the value of one function into variable spot of the second function. Consider and are two functions, if we put the value of into at the variable position of) i.e., the new formed function will be called composition of and written as or and read as f-compose-g of x [Purplemath (2014)]. We define the following functions: Note that by putting the values of both functions, we get;Now, we solve these by calculating L.C.M process; Now to find we put in Evaluate the following two compositions: A: B: A. is a composition function of and . It can be calculated by putting the value of into in the place of ;So, the required composition functions is as under;B. is a composition function of and It can be calculated by putting the value of into in the place of x;So, the required composition functions is as under;Graph the function and transform it so that the graph is moved 6 units to the right and 7 units down. The graph of the given function can be plotted by taking random values of x variable on x axis and identifying points by calculating corresponding y coordinate. Also, as we know that is the equation of parabola and subtracting 3 from will just shift the basic parabola three points downwards. Following is the three points shifted graph, representing Now in order to transform the graph fu

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