A-LevelMathematicsFunctions9709/12 · Oct/Nov 2018 · Q97 Marks
The function f is defined by f : x → 2x² – 12x + 7 for x ∈ R.
- (i)Express 2x² – 12x + 7 in the form 2(x + a)² + b, where a and b are constants.[2]
- (ii)State the range of f.[1]
- (iii)The function g is defined by g : x → 2x² – 12x + 7 for x ≤ k. State the largest value of k for which g has an inverse.[1]
- (iv)Given that g has an inverse, find an expression for g⁻¹(x).[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2018). The mark or mark type is shown in brackets.
- [B1] 2(x - 3)²
- [B1] -11
- [B1FT] Range (of f or y) ≥ 'their – 11'
- [B1FT] (k =) -"their a” also allow x or k ≤ 3
- [*M1] y = 2(x - 3)² - 11 → y + 11 = 2(x - 3)²
- [DM1] (y + 11)/2 = (x - 3)² → x - 3 = ±√((y + 11)/2)
- [A1] x = 3 - √((y + 11)/2)
Write your answer and get it marked
On Oracle Prep you can write or photograph your own answer and have it marked by AI against this mark scheme, with feedback on what you missed.
Sign up free →