A-LevelMathematicsFunctions9709/12 · Oct/Nov 2010 · Q77 Marks
The function f is defined by f(x) = x² – 4x +7 for x > 2.
- (i)Express f(x) in the form (x – a)² + b and hence state the range of f.[3]
- (ii)Obtain an expression for f⁻¹(x) and state the domain of f⁻¹.[3]
- (iii)The function g is defined by g(x) = x – 2 for x > 2. The function h is such that f = hg and the domain of h is x > 0. Obtain an expression for h(x).[1]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2010). The mark or mark type is shown in brackets.
- [M1] (x-2)² Must be '-2' ± k
- [A1] (x-2)² + 3 co
- [B1√] f(x) > 3 ft on their '3'
- [M1] x − 2 = (±) √y-3 ± not required for M mark
- [A1] f⁻¹(x) = 2 + √x -3 f(x) + removal of minus sign needed
- [B1√] domain is x >3 ft domain of f⁻¹ = range of f or for f⁻¹
- [B1] h(x) = x² + 3 co
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