Question

Determine whether these two functions are inverses.​

Answer 1

Yes,these two functions are the inverse of each other.

Explanation:

They way of finding if two functions (
`f(x)\,\,and\,\,g(x)` ) are the inverse of each other is by studying if their composition renders in fact the identity. That is, we see if:

`f(x) \,o \,g(x)=f(g(x))=x`

in our case:

`f(g(x))=(1)/(g(x)+4) -9\\f(g(x))=(1)/(((1)/(x+9) -4)+4)-9\\f(g(x))=(1)/((1)/(x+9) )-9\\f(g(x))={x+9} -9\\f(g(x))=x`

The composition does render the identity, therefore, these two functions are indeed the inverse of each other