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Functions and Graphs

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Question 122

The functions f f\,f and g g\,g are defined for all real values of x x\,x by

f(x)=x3andg(x)=x2−1 f(x) = x^3 \quad \text{and} \quad g(x) = x^2 - 1 f(x)=x3andg(x)=x2−1
a.

Write down expressions for fg(x)fg(x)fg(x) and gf(x)gf(x)gf(x)

[2]
b.

Show that gf(x)−fg(x)=3x2(x2−1)gf(x) - fg(x) = 3x^2(x^2 - 1)gf(x)−fg(x)=3x2(x2−1)

[2]
c.

Hence find the values of x x\,x for which gf(x)−fg(x)=18gf(x) - fg(x) = 18gf(x)−fg(x)=18

[4]
Markscheme

Functions and Graphs Questions

  1. A Level
  2. /Maths
  3. /Functions and Graphs

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.

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