The functions f f\,f and g g\,g are defined by
f:x→ln(2x−1),x∈R,x>12 f: x \rightarrow \ln(2x - 1), \quad x \in \mathbb{R}, x > \frac{1}{2} f:x→ln(2x−1),x∈R,x>21 g:x→4x−1,x∈R,x≠1 g: x \rightarrow \frac{4}{x-1}, \quad x \in \mathbb{R}, x \neq 1 g:x→x−14,x∈R,x=1Find the exact value of fg(3)fg(3)fg(3)
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 ∣4x−1∣=2\displaystyle | \frac{4}{x-1} | = 2∣x−14∣=2
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.