O-LevelAdditional MathematicsFunctions4037/11 · May/June 2016 · Q69 Marks
The function f is defined by f(x) = 2 - √x+5 for -5 ≤ x < 0.
- (i)Write down the range of f.[2]
- (ii)Find f⁻¹(x) and state its domain and range.[4]
- (iii)Solve fg(x) = 0 .[3]
Mark scheme
Marking points from the official mark scheme (May/June 2016). The mark or mark type is shown in brackets.
- [1] f(x) < 2
- [1] 2 - √5 < f(x)
- [1] f⁻¹(x) = (2-x)² - 5
- [1] f⁻¹(x) = (2-x)² - 5
- [1] Domain 2 - √5 < x < 2
- [1] Range y or -5 < f⁻¹(x) < 0
- [1] fg(x) = f(4/x)
- [1] = 2 - √(4/x + 5)
- [1] x = -4
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