Math 1201 week 4 Learning Journal Entry 2021 composite and inverse functions PDF

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Math 1201 week 4 Learning Journal Entry 2021 composite and inverse functions...

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WEEK 4 Reflect on the concept of composite and inverse functions. Composite functions are functions within other functions where the output of one function is the input for another function. Inverse functions are functions to bring you back to the origin, like reversing and is also a reflected function on a graph. What concepts (only the names) did you need to accommodate these concepts in your mind? For composite functions, I needed to understand composite function notations, how to combine functions, create, evaluate, and interpret composite functions, decompose functions, find out if two functions are commutative, and graph them. As for inverse functions, I needed to know how to verify if two functions are inverse of each other, solve to find the inverse function given a function, find the domain and range of inverse functions, interpret inverse functions given a table or graph, and graph inverse functions using restricted domains and reflections. What are the simplest composite and inverse functions you can imagine? Simple composite function: f(g(x)) where f(x)=x+1 and g(x)=x+1 so f(g(x))=(x+1)+1 Simple inverse function: f(x)=x-2 y=x-2 x=y-2 x+2=y So the inverse function would be f^1(x)=x+2 In your day to day, is there any occurring fact that can be interpreted as composite and inverse functions? Composite functions: I used to work in the fashion industry where we had promos and discounts in stores. If a customer bought minimum 2 products, they could get a discount of 30%. We also had promo codes that you could use in the store. So the first function would be to find the price after the initial 30% discount then the composite function would be used to find the final price after entering the promo code. Inverse functions: Since distance, time, and speed are in a triangle equation where distance = speed x time. The function could be d(t)=5x if the person was walking at an average of 5kmph and x refers to the time then the inverse function would be d^-1(x)=x/5 to find the time given the distance and speed. Another example is ctrl z on word documents as it reverses the function to output the original information. What strategy are you using to get the graph of composite and inverse functions?

I am using Desmos (Desmos, 2011) to get the graphs of composite and inverse functions as it is the easiest and clearest way to see and analyze these graphs. I also draw rough graphs on my whiteboard to solidify information in my mind. References Desmos. (2011). [Advanced graphing calculator]. Desmos, Inc. https://www.desmos.com...