A function f is defined by f(x) = 5/(1-3x) for x ≥ 1.

Mark scheme

Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.

1. [1] B1 For (i): Correct numerator after differentiation, e.g., -5 × -3
2. [1] B1 For (i): Correct denominator after differentiation, e.g., (1-3x)² or (1-3x)⁻²
3. [1] B1 For (ii): Function is increasing (since f'(x) > 0 for x ≥ 1)
4. [1] M1 For (iii): Attempts to make x the subject from y = f(x)
5. [1] A1 For (iii): Correct expression for f⁻¹(x) = (x-5)/(3x) (or 1/3 - 5/(3x))
6. [1] B1 For (iii): Correct range of f⁻¹(x) as y ≥ 1
7. [1] B1 For (iii): Correct domain of f⁻¹(x) as x ≥ -2.5
8. [1] B1 For (iii): Correct domain of f⁻¹(x) as x < 0