A-LevelMathematicsFunctions9709/12 · Oct/Nov 2020 · Q56 Marks
Functions f and g are defined by f(x) = 4x – 2, for x ∈ R, g(x) = 4/(x+1), for x ∈ R, x ≠ −1.
- (a)Find the value of fg(7).[1]
- (b)Find the values of x for which f⁻¹(x) = g⁻¹(x).[5]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [B1] 0
- [B1] (f⁻¹(x)) = (x+2)/4 OE. Sight of correct inverses.
- [B1] (g⁻¹(x)) = (4-x)/x or 4/x - 1 OE. Sight of correct inverses.
- [B1] Equating inverses and simplifying.
- [M1] Correct attempt at solution of their 3-term quadratic - factorising, completing the square or use of formula.
- [A1] (x =) 2 or -8 Do not accept answers obtained with no method shown.
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