The functions f f\,f and g g\,g are defined for all real values of x x\,x by
f(x)=x3f(x) = x^3f(x)=x3 and g(x)=x2−1g(x) = x^2 - 1g(x)=x2−1
Write down expressions for fg(x)fg(x)fg(x) and gf(x)gf(x)gf(x).
Hence find the values of x x\,x for which gf(x)−fg(x)=18gf(x) - fg(x) = 18gf(x)−fg(x)=18.
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.