# Composition and Inverse.

May 13th, 2015
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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.

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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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