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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 24

The functions f f\,f and g g\,g are defined by

f:x↦ln⁡(3x−2)f : x \mapsto \ln(3x - 2)f:x↦ln(3x−2), x∈Rx \in \mathbb{R}x∈R, x>23\displaystyle x > \frac{2}{3}x>32​

g:x↦3x−2\displaystyle g : x \mapsto \frac{3}{x - 2}g:x↦x−23​, x∈Rx \in \mathbb{R}x∈R, x≠2x \neq 2x=2

a.

Find the exact value of fg(3)fg(3)fg(3).

[2]
b.

Find an expression for f−1(x)f^{-1}(x)f−1(x) and, using set notation, state its domain.

[3]
c.

Find the exact values of x x\,x for which ∣g(x)∣=4|g(x)| = 4∣g(x)∣=4.

[2]
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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