A-LevelMathematicsFunctions9709/12 · Oct/Nov 2023 · Q88 Marks
Functions f and g are defined by f(x) = (x + a)² – a for x ≤ −a, g(x) = 2x - 1 for x ∈ R, where a is a positive constant.
- (a)Find an expression for f⁻¹(x).[3]
- (b)(i)State the domain of the function f⁻¹.[1]
- (b)(ii)State the range of the function f⁻¹.[1]
- (c)Given that a = 7/2, solve the equation gf(x) = 0.[3]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2023). The mark or mark type is shown in brackets.
- [*M1] x and y may be interchanged initially. Allow ± errors for these method marks.
- [DM1]
- [A1] OE Must choose negative root.
- [B1] Ignore infinity limit if included.
- [B1] Ignore negative infinity limit if included.
- [B1] OE Alternatively, [gf(x)=0>]f(x)= -1/2.
- [M1] OE Solving their three term quadratic equation as far as two solutions or correctly selecting the negative root only. Alternatively, ±(1/2) ± (7/2) ± (7/2)
- [A1] If B1M0 scored then award SCB1 for the correct final answer.
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