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)

Graph of 7(iI)
Graph of 7(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

KS Comments:

The term “self-inverse” made some students confused as they were unsure what it means. It means that g is its own inverse. The easiest way to draw this curve is to first identify the asymptotes, then substitute x = 0 and y = 0 to resolve for the axial intercepts. For (iii), students must learn to describe fully, using the correct key words and terms.

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