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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 317

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≤0
a.

Solve the equation hq(x)=4hq(x) = 4hq(x)=4.

[3]
b.

Find h−1(x)h^{-1}(x)h−1(x).

[3]
c.

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.

[4]
Markscheme

1.5 B: Algebra and functions Questions

  1. A Level
  2. /Maths
  3. /1.5 B: Algebra and functions

532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, 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). Each one has a worked solution and a mark scheme showing where the marks go.

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