O-LevelAdditional MathematicsFunctions4037/21 · May/June 2018 · Q56 Marks
The function f is defined by f(x) = 1/(2x-5) for x > 2.5.
- (i)Find an expression for f⁻¹(x).[2]
- (ii)State the domain of f⁻¹(x).[1]
- (iii)Find an expression for f²(x), giving your answer in the form ax + b / cx + d where a, b, c and d are integers to be found.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [1] (i) Putting y = f(x), changing subject to x and swopping x and y or vice versa
- [1] (i) f⁻¹(x) = (1/x + 5)/2 or (5x+1)/(2x) oe isw
- [1] (ii) x > 0 oe
- [1] (iii) 1/(2(1/(2x-5))-5) oe
- [1] (iii) 1 / ((2-10x+25)/(2x-5)) oe
- [1] (iii) (2x-5) / (-10x+27) or (5-2x)/(10x-27)
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