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.
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.