O-LevelAdditional MathematicsFunctions4037/22 · Oct/Nov 2014 · Q46 Marks
The functions f and g are defined for real values of x by f(x) = √x - 1 - 3 for x > 1, g(x) = (x - 2) / (2x - 3) for x > 2.
- (i)Find gf(37).[2]
- (ii)Find an expression for f⁻¹(x).[2]
- (iii)Find an expression for g⁻¹(x).[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2014). The mark or mark type is shown in brackets.
- [B1] (i) f(37)=3 or gf(x) = (√(x-1)-3-2) / (2(√(x-1)-3)-3)
- [B1] (i) gf(37) = (3-2)/(6-3) = 1/3
- [M1] (ii) y=√x-1-3 → (y+3)² = x-1. Rearrange and square in any order.
- [A1] (ii) (x+3)² +1 = f⁻¹(x) oe isw. Interchange x and y and complete.
- [M1] (iii) y = (x-2)/(2x-3) → 2xy-3y = x-2 → 2xy-x = 3y-2. Multiply and collect like terms.
- [A1] (iii) (3x-2)/(2x-1) = g⁻¹(x) oe. Interchange and complete. Mark final answer.
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