O-LevelAdditional MathematicsFunctions4037/21 · May/June 2013 · Q118 Marks
A one-one function f is defined by f(x) = (x - 1)² – 5 for x ≥ k.
- (i)State the least value that k can take.[1]
- (ii)For this least value of k write down the range of f,[1]
- (iii)find f⁻¹(x),[2]
- (iv)sketch and label, on the axes below, the graph of y = f(x) and of y = f⁻¹(x), [Figure 11.1][2]
- (v)find the value of x for which f(x) = f⁻¹(x).[2]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2013). The mark or mark type is shown in brackets.
- [1] (i) 1
- [1] (ii) f > -5
- [1] (iii) Method of inverse
- [1] (iii) 1 + √x+5
- [1] (iv) f: Positive quadratic curve correct range and domain
- [1] (iv) f⁻¹: Reflection of f in y = x
- [1] (v) Arrange f (x) = x or f⁻¹ (x) = x to 3 term quadratic = 0
- [1] (v) 4 only www
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 →