Answer to Question #337341 in Algebra for solomon

Question

Reflect on the concept of composite and inverse functions. What concepts (only the names) did you need to accommodate these concepts in your mind? What are the simplest composite and inverse functions you can imagine? In your day to day, is there any occurring fact that can be interpreted as composite and inverse functions? What strategy are you using to get the graph of composite and inverse functions?

Answer 1

Exponential and logarithmic functions epitomize the concept of inverse functions. I personally never found the concept of composite functions to be difficult to understand. Couldn't polynomials be described as composite functions, because it is essentially the sum of all the differently powered terms? I believe that the phenomena of population growth can me modeled by exponential functions in many cases. If your struggling with these concepts, then just focus on the simplest cases of them. Exponents and logarithms are terms and concepts that will help you understand both inverse and composite functions if you are familiarized with them. If your struggling with graphing a composite function, then graph out the constituent functions of it. Afterwards, add up the outputs of them at a certain x-values, and make coordinate points where the sum of the outputs are the y-value of the coordinate. You can graph the inverse of a function by reflecting with respect to the line y = x.