The function f f\,f is defined by
f(x)=∣2x∣+3f(x) = |2x| + 3f(x)=∣2x∣+3 for x∈Rx \in \mathbb{R}x∈R
The function g g\,g is defined by
g(x)=ln(x−1)g(x) = \ln(x - 1)g(x)=ln(x−1)
where g g\,g has its greatest possible domain.
Using set notation, state the range of fff.
State the domain of ggg.
The composite function h h\,h is given by h(x)=gf(x)h(x) = gf(x)h(x)=gf(x) for x∈Rx \in \mathbb{R}x∈R.
Write down an expression for h(x)h(x)h(x) in terms of xxx.
Determine whether h h\,h has an inverse. Fully justify your answer.
The function k k\,k is defined by k(x)=gf(x)k(x) = gf(x)k(x)=gf(x) for x≥0x \geq 0x≥0. Find k−1(x)k^{-1}(x)k−1(x) and, using set notation, state its domain.
532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.