Answer
$ \frac{x-3}{2}$
Work Step by Step
To find $(f\circ g)^{-1}$ we can either calculate $fog$ and find its inverse or we can use the relation:
$(f\circ g)^{-1} = g^{-1}of^{-1}$
Let's do it by the first method.
First, we calculate $(g\circ f)(x) = g(f(x)) = g(x+4) = 2(x+4)-5 = 2x+3$
To find the inverse of f(x), we replace $f(x)$ by $x$ and $ x$ by $ f^{-1}(x)$ and solve for $ f^{-1}(x)$.
So, $x = 2(g\circ f)^{-1}(x)+3 $
or $(g\circ f)^{-1}(x) = \frac{x-3}{2}$
