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y = 1/(2x - 4) + 3

The matrix gives x' = ax + c and y' = y + d

ie x =(x' - c)/a and y= y' - d

Now choose a, c, d to transform into y' = f(x') = 1/x'

Substituting gives

y' - d = 1/(2(x' - c)/a - 4) + 3

y' = 1/(2x'/a - 2c/a- 4) + 3 + d = 1/x'

Clearly for y' = 1/x'

2/a = 1

-2c/a- 4 = 0

3 + d = 0

Giving a = 2 , c = -4, d = -3