The functions f f\,f and g g\,g are defined by
f:x→ln(5x−2),x∈R,x>25 f: x \rightarrow \ln(5x - 2), \quad x \in \mathbb{R}, x > \frac{2}{5} f:x→ln(5x−2),x∈R,x>52 g:x→2x−4,x∈R,x≠4 g: x \rightarrow \frac{2}{x-4}, \quad x \in \mathbb{R}, x \neq 4 g:x→x−42,x∈R,x=4Find the exact value of fg(6)fg(6)fg(6)
Find an expression for f−1(x)f^{-1}(x)f−1(x) and state its domain
Sketch the graphs of f(x)f(x)f(x) and f−1(x)f^{-1}(x)f−1(x) on the same diagram
Sketch the graph of y=∣g(x)∣y = |g(x)|y=∣g(x)∣
Find the exact values of ∣2x−4∣=4\displaystyle | \frac{2}{x-4} | = 4∣x−42∣=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.