The function f is such that f(x) = 3x² – 1 for –10 ≤ x ≤ 8. Find the range of f.

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2013). The mark or mark type is shown in brackets.

1. [M1] (a) (i) for substitution of either x = -10 or x = 8, may be seen on diagram
2. [B1] Min point at (0, -1) or when y = -1
3. [A1] Must have ≤ for A1, do not allow x (Range: -1 ≤ y ≤ 299)
4. [B1] (a) (ii) Allow any domain which will make f a one-one function (e.g. x ≥ 0 or equivalent)
5. [M1] (b) (i) for complete method to find the form inverse function, must involve ln or lg if appropriate. May still be in terms of y.
6. [A1] must be in terms of x (g⁻¹(x) = ln((x+2)/4))
7. [M1] (b) (ii) for correct order (gh(x) = g(ln 5x))
8. [A1] for correct expression 4e^(ln 5x) - 2
9. [A1] for correct solution from correct working (x = 1)
10. Or:
11. [M1] for correct order (h(x) = g⁻¹(18))
12. [A1] for correct equation (ln 5x = ln 5)
13. [A1] for correct solution from correct working (x = 1)