Functions f and g are defined as follows

$\displaystyle

f(x) = 2x + 3, x\epsilon\Re $ and $\displaystyle g(x) = \frac{1}{x-1}, x\epsilon\Re $, $\displaystyle x$$\displaystyle \ne 1$

(i) Find the expression for the inverse function f^-1$\displaystyle (x)$

(ii) Find the expression for the composite function $\displaystyle gf$$\displaystyle (x)$

(iii) Solve the equation f^-1$\displaystyle (x)$ $\displaystyle =$$\displaystyle gf(x)-1$

I got:

(i)

$\displaystyle y = 2x+3 $

$\displaystyle y - 3 = 2x$

$\displaystyle \frac{y-3}{2} = x $

$\displaystyle \frac{x-3}{2} = y $?

(ii)

And I got $\displaystyle g(f(x)) = \frac{1}{2x+2}$

Am i correct? If not, please help.