All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)

Let $y = \frac{x+k}{x-1}$

$xy - y = x + k$

$x = \frac{y+k}{y-1}$

$g^{-1}: x \rightarrow \frac{x+k}{x-1}$

$\therefore$, g is self inverse.

(ii)

(iii)
Line of symmetry is y = x.

Required transformations are as follow, in order.
1. Translate by 1 unit in the positive x-axis
2. Scale by factor (k+1) units parallel to the y-axis
3. Translate by 1 unit in the direction of the positive y-axis