The signal transfer function hhh and the power decay profile qqq are defined by
h(x)=5x+4x−2,x∈R,x≠2 h(x) = \frac{5x + 4}{x - 2}, \quad x \in \mathbb{R}, x \neq 2 h(x)=x−25x+4,x∈R,x=2 q(x)=3−x2,x∈R,x≤0 q(x) = 3 - x^2, \quad x \in \mathbb{R}, x \le 0 q(x)=3−x2,x∈R,x≤0Solve the equation hq(x)=4hq(x) = 4hq(x)=4.
Find h−1(x)h^{-1}(x)h−1(x).
Sketch and label, on the same axes, the curve with equation y=q(x)y = q(x)y=q(x) and the curve with equation y=q−1(x)y = q^{-1}(x)y=q−1(x). Show on your sketch the coordinates of the points where each curve meets or cuts the coordinate axes.
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.
