The signal transfer function hhh and the power decay profile qqq are defined by
h(x)=5x+4x−2,x∈R,x≠2h(x) = \frac{5x + 4}{x - 2}, \quad x \in \mathbb{R}, x \neq 2h(x)=x−25x+4,x∈R,x=2
q(x)=3−x2,x∈R,x≤0q(x) = 3 - x^2, \quad x \in \mathbb{R}, x \le 0q(x)=3−x2,x∈R,x≤0
Solve 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 Edexcel A Level Maths 2.4 Inverse Functions with exam-style questions for A Level Maths. 41 questions, matched to the Edexcel A Level Maths (9MA0) 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.