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Functions and Graphs

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Question 105

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

f(x)=3x2−5x and g(x)=4x+8 f(x) = 3x^2 - 5x \text{ and } g(x) = 4x + 8 f(x)=3x2−5x and g(x)=4x+8
a.

Find the range of fff, giving your answer in exact form.

[3]
b.

Give a reason why f f\,f has no inverse.

[1]
c.

Given that gf(2)=g−1(a)gf(2) = g^{-1}(a)gf(2)=g−1(a), where a a\,a is a constant, determine the value of aaa.

[3]
d.

Determine the set of values for which f(x)>g(x)f(x) > g(x)f(x)>g(x). Give your answer exactly in set notation.

[3]
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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