Question

Given the following functions:

Answer 1

Answer:

The composition of the two functions are $(fog)(x)=f(g(x))=x^2-6x+9$ and $(gof)(x)=g(f(x))$

Step-by-step explanation:

Given two functions are

$f(x)=^2$

and $g(x)=x-3$

Now to find the composition of f and composition of g and f

ie, $(fog)(x)=f(g(x))$

and $(gof)(x)=g(f(x))$

$(fog)(x)=f(g(x))$

           $=f(x-3)$

           $=(x-3^2)$

         Now to find the composition of f and composition of  $=x^2-2x(3)+3^2$

$(fog)(x)=x^2-6x\div 9$

$(gof)(x)=g(f(x))$

$=g(x^2)$

$(gof)(x)=x^2-3$

The composition of the two functions are $(gof)(x)=g(f(x))=x^2-3$