The function f is defined by f(x) = 3 tan(1/2 x) - 2, for -1/2 π ≤ x ≤ 1/2 π.

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

1. 3tan(1/2 x) = -2 → tan(1/2 x) = -2/3
2. [M1] Attempt to obtain tan(1/2 x) = k from 3tan(1/2 x) + 2 = 0
3. 1/2 x = -0.6 (-0.588) → x = -1.2
4. [M1 A1] tan⁻¹ k. Seeing 1/2 x = -33.69° or x= -67.4° implies M1M1. Extra answers between -1.57 &1.57 lose the A1. Multiples of π are acceptable (eg – 0.374π)
5. y + 2 / 3 = tan(1/2 x)
6. [M1] Attempt at isolating tan(1/2x)
7. → f⁻¹(x) = 2tan⁻¹((x+2)/3)
8. [M1 A1] Inverse tan followed by × 2. Must be function of x for A1.
9. Domain = -5, 1
10. [B1 B1] Values stated B1 for -5, B1 for 1.
11. A tan graph through the first, third and fourth quadrants. (B1)
12. An invtan graph through the first, second and third quadrants.(B1)
13. Two curves clearly symmetrical about y = x either by sight or by exact end points. Line not required. Approximately in correct domain and range. (Not intersecting.) (B1)
14. Labels on axes not required.