Let f(x)=(x/x+3).
Find Domain
Find f^(-1) and its domain
Verify f*f^(-1)=f^(-1)*f=x
Find (f(x+h)-f(x))/h.
I bet you mean
y = x/(x+3)
The denominator is 0 when x = -3 so x = -3 is not in our domain. Otherwise the domain is all real numbers.
Inverse
x = y/(y+3)
x y + 3 x = y
y(x-1) = -3 x
y = -3x/(x-1)
domain is all real numbers except x = 1
f[f^(-1)] = f[-3x/(x-1) ]
= [-3x/(x-1) ] /{ [-3x/(x-1) ]+3 }
[-3x/(x-1) ]/{[-3x/(x-1) ]+3(x-1)/(x-1)}
= -3x/{-3x +3x -3}
= -3x/-3
= x
etc