The functions f f\,f and g g\,g are defined by
f:x→ln(3x−2),x∈R,x>23 f : x \rightarrow \ln(3x - 2), \quad x \in \mathbb{R}, x > \frac{2}{3} f:x→ln(3x−2),x∈R,x>32 g:x→3x−2,x∈R,x≠2 g : x \rightarrow \frac{3}{x-2}, \quad x \in \mathbb{R}, x \neq 2 g:x→x−23,x∈R,x=2Verify that fg(3)=ln7fg(3)=\ln 7fg(3)=ln7
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 ∣3x−2∣=4\displaystyle | \frac{3}{x-2} | = 4∣x−23∣=4
471 exam-style questions on Edexcel A Level Maths Functions and Graphs, covering 2.1 The Modulus Function, 2.2 Functions and Mappings, 2.3 Composite Functions, 2.4 Inverse Functions, 2.5 y=|f(x)| and y=f(|x|), 2.6 Combining Transformations, and 2.7 Solving Modulus Problems. Each one has a worked solution and a mark scheme showing where the marks go.