A-LevelMathematicsFunctions9709/12 · Feb/Mar 2019 · Q810 Marks
Express x² – 4x + 7 in the form (x + a)² + b.
- (i)Express x² – 4x + 7 in the form (x + a)² + b.[2]
- (ii)The function f is defined by f(x) = x² – 4x + 7 for x < k, where k is a constant. State the largest value of k for which f is a decreasing function.[1]
- (iii)The value of k is now given to be 1. Find an expression for f⁻¹(x) and state the domain of f⁻¹.[3]
- (iv)The function g is defined by g(x) = 2/(x-1) for x > 1. Find an expression for gf(x) and state the range of gf.[4]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.
- [B1DB1] [(x-2)²]+[3]
- [B1] Largest k is 2 Accept k ≤2
- [M1] y=(x-2)² +3 ⇒ x−2=(±)√y-3
- [A1B1] ⇒f⁻¹(x)=2-√x−3 for x>4
- [B1] gf(x) = 2 / ( (x-2)² + 3 - 1 )
- [M1A1] gf(x) = 2 / ( (x-2)² + 2 )
- [B1] range of gf(x) is 0 < gf(x) < 2/3
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