Anybody good in math doing function problems? I need help...thanks.. anyone?

Question

Let f(x) = x−1x+3. Find its inverse function by exchanging x and y in the equation y = f(x) and solving for y. Call the inverse g(x). Compute f o g(x) and g o f(x) to show that f and g are inverse functions. What is the domain of g? So, what is the range of f?


I got the inverse it's f^-1= -3x-1/x-1 correct me if I'm wrong. But I'm not sure about computing the f o g(x) and g o f(x).

Answer 1

I assume u mean f(x)=(x-1)/(x+3)
y=(x-1)/(x+3)
y(x+3)=x-1
x*y+3y=x-1
x*y-x=-3y-1
x(y-1)=-3y-1
x=(-3y-1)/(y-1)
now change x and y
y=(-3x-1)/(x-1)
I wish it helps.
Sorry for my English.