Consider the functions f(x)= 2x+4/x+9 and g(x)= 9x-4/2-x

Question

a) Find f(g(x)).

Give any values of x taht need to be excluded from f(g(x)).

b) Find g(f(x)).

c) Determine wheather the function f and g are inverses of each other.

Answer 1

The functions are

a)

                

              

           

          

         

The domian of composition is all real numbers with the exclusion of 2.

b)

               

             

            

          

         

c)

Two functions f and g are inverse functions if and only if both of their compositions are the identity function.

That means [f o g](x) = x and [g o f](x) = x.

In this case

Therfore, the functions f and g are inverse of each other.