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?

The Learning Journal entry should be a minimum of 400 words and not more than 750 words.

Answer 1

Composition of functions.

Let and

be two functions then function f takes a_n element

to an element f(x)= , and this y is durther taken by g to an element .

So Z=g(y)=g(f(x))=(g o f)(n)

then, for each , a rule which associated, a unique element z=g(f(x)) of C.

This rule is therefore, a function from A to C.

We denote this function g o f   (read as 'g composition f') and call it the "composite function of f an g"/

Thus,

and be any two functions, then the composite function of f & g is denoted by g o f and it is function

gof: defined by (gof)(x)=g(f(x))

gof is defined if:

i)Domain(gof)=Domain f

and Codomain(gof)=Codomain(g)

ii) gof is well defined only if range

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