O-LevelAdditional MathematicsFunctions4037/12 · May/June 2012 · Q109 Marks
It is given that f(x) = 1/(2+x) for x ≠ −2, x ∈R. Find f'(x).
- (a)(i)It is given that f(x) = 1/(2+x) for x ≠ −2, x ∈R. Find f'(x).[1]
- (a)(ii)Find f⁻¹(x).[2]
- (a)(iii)Solve f²(x) = −1.[3]
- (b)(i)The functions g, h and k are defined, for x ∈ R, by g(x) = 1/(x+5), x ≠ -5, h(x) = x² -1, k(x) = 2x + 1. Express the following in terms of g, h and/or k. 1 / ((x²-1) +5)[1]
- (b)(ii)2 / (x+5) + 1[2]
Mark scheme
Marking points from the official mark scheme (May/June 2012). The mark or mark type is shown in brackets.
- [B1] First B1 may be implied by a correct f''(x)
- [B1] If done by quotient rule, allow unsimplified
- [M1] M1 for a valid attempt at the inverse
- [A1] A1 must be in correct form, allow y = ...
- [M1] M1 for correct attempt at f²(x)
- [DM1] DM1 for attempt at solution of f²(x) = −1
- [A1] A1 for x = -7/3 or equivalent
- [B1] B1 for either form
- [B1] B1 for either form
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