The functions f f\,f and g g\,g are defined by
f:x↦ln(3x−2)f : x \mapsto \ln(3x - 2)f:x↦ln(3x−2), x∈Rx \in \mathbb{R}x∈R, x>23\displaystyle x > \frac{2}{3}x>32
g:x↦3x−2\displaystyle g : x \mapsto \frac{3}{x - 2}g:x↦x−23, x∈Rx \in \mathbb{R}x∈R, x≠2x \neq 2x=2
Find the exact value of fg(3)fg(3)fg(3).
Find an expression for f−1(x)f^{-1}(x)f−1(x) and, using set notation, state its domain.
Find the exact values of x x\,x for which ∣g(x)∣=4|g(x)| = 4∣g(x)∣=4.
181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.