The function fff is defined by
f(x)=3x+2x−3,x∈R,x≠3 f(x) = \frac{3x + 2}{x - 3}, \quad x \in \mathbb{R}, x \neq 3 f(x)=x−33x+2,x∈R,x=3(i) Find f−1(x)f^{-1}(x)f−1(x). (a) (ii) Write down an expression for ff(x)ff(x)ff(x).
The function ggg is defined by
g(x)=x2−4x2,x∈R,0≤x≤6 g(x) = \frac{x^2 - 4x}{2}, \quad x \in \mathbb{R}, 0 \leq x \leq 6 g(x)=2x2−4x,x∈R,0≤x≤6(b) (i) Find the range of ggg. (b) (ii) Determine whether ggg has an inverse. Fully justify your answer.
Show that
gf(x)=−3x2+40x+282x2−12x+18 gf(x) = \frac{-3x^2 + 40x + 28}{2x^2 - 12x + 18} gf(x)=2x2−12x+18−3x2+40x+28It can be shown that fgfgfg is defined for a restricted domain of ggg. If the denominator of fg(x)fg(x)fg(x) is given by x2−4x−6x^2 - 4x - 6x2−4x−6, find the value of aaa that must be excluded from the domain 0≤x≤60 \leq x \leq 60≤x≤6 such that fg(x)fg(x)fg(x) is undefined. Fully justify your answer.
Practise AQA A Level Maths 1.5 B: Algebra and functions with exam-style questions for A Level Maths. 358 questions 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), matched to the AQA A Level Maths (7357) specification and written in Paper 1, Paper 2 and Paper 3 style. Every question includes a full worked solution and mark scheme, so you can see where marks are awarded rather than just whether you got the answer right.
