O-LevelAdditional MathematicsFunctions4037/12 · Oct/Nov 2019 · Q57 Marks
(a) It is given that f : x ↦ √x for x ≥ 0, g : x ↦ x + 5 for x ≥ 0. Identify each of the following functions with one of f⁻¹, g⁻¹, fg, gf, f², g². (b) It is given that h(x) = a + b/x² where a and b are constants.
- (a)(i)√x+5[1]
- (a)(ii)x-5[1]
- (a)(iii)x²[1]
- (a)(iv)x+10[1]
- (b)(i)Why is -2 ≤ x ≤ 2 not a suitable domain for h(x)?[1]
- (b)(ii)Given that h(1) = 4 and h′(1) = 16, find the value of a and of b.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2019). The mark or mark type is shown in brackets.
- [1] B1 fg
- [1] B1 g⁻¹
- [1] B1 f⁻¹
- [1] B1 g²
- [1] B1 Undefined at x = 0 oe
- [1] M1 For attempt at h(1) and differentiation to obtain h'(1), must have the form h'(x) = p/x³ oe
- [1] A1 For both b = -8, a = 12
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