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.
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.