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1.5 B: Algebra and functions

1.5 B: Algebra and functions

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Question 332

The functions fff and ggg are defined by

f(x)=3+4ln⁡x,x>0 f(x) = 3 + 4\ln x, \quad x > 0 f(x)=3+4lnx,x>0 g(x)=8x−42x+1,x>12 g(x) = \frac{8x - 4}{2x + 1}, \quad x > \frac{1}{2} g(x)=2x+18x−4​,x>21​
a.

Find f−1(15)f^{-1}(15)f−1(15).

[2]
b.

Use differentiation to prove that ggg is an increasing function.

[3]
c.

Find g−1(x)g^{-1}(x)g−1(x).

[3]
d.

Find the range of the composite function fgfgfg.

[3]
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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