Answer:
Yes,these two functions are the inverse of each other.
Step-by-step explanation:
They way of finding if two functions ([tex]f(x)\,\,and\,\,g(x)[/tex] ) are the inverse of each other is by studying if their composition renders in fact the identity. That is, we see if:
[tex]f(x) \,o \,g(x)=f(g(x))=x[/tex]
in our case:
[tex]f(g(x))=\frac{1}{g(x)+4} -9\\f(g(x))=\frac{1}{(\frac{1}{x+9} -4)+4}-9\\f(g(x))=\frac{1}{\frac{1}{x+9} }-9\\f(g(x))={x+9} -9\\f(g(x))=x[/tex]
The composition does render the identity, therefore, these two functions are indeed the inverse of each other
