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

Composite of functions:

Definition: For any two functions f: A---> B and

g: B--->C the composition is defined as

Concepts you need:

Function, domain, codomain and range.

Real life example:

Suppose is a function which puts socks on your feet and is a function which puts shoes on ur feet (with socks). Then to get ready to the office, you must apply the composition . Think about using . The later composition function is not defined though as the output of 'g' is not the input for 'f'.

Inverse function:

Definition: For a function f: A---> B the inverse function is

g: B---> A such that

where are identity functiona on set A and set B respectively.

Real life example:

For the above function in the example of inverse function, the inverse of 'f' will be a function

which is unwearing socks from the feet.

Further the inverse of composition is given by law:

LHS represents the inverse function of "getting ready on shoes" actually which must be applied when one gets back to home at evening and start unwearing the shoes. RHS describes the process of applying

first which is taking off your shoes first and then

which is unwearing socks later.

Think on the same lines that why

.