g(x)=y=(9x-2)/(-4x+5)

9x-2=y(5-4x)

x(9+4y)=5y+2

x=(5y+2)/(4y+9)

That is, the inverse function f(x)=(5x+2)/(4x+9)

Because, 4x+9≠0, x≠-9/4.

So the domain of the inverse function is x∈R, x≦-9/4.

According to the properties of inverse function, the domain of inverse function is the domain of original function.

The domain of that original function is x≠5/4,

So the range of the inverse function is (negative infinity, 5/4)U(5/4, positive infinity).