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Functions and Graphs

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Question 20

A sketch of y = g(x) with a decreasing straight-line branch joined to an upward-curving branch at a filled point.

The diagram shows a sketch of y=g(x)y = g(x)y=g(x), where

g(x)={8−2xx<2(x−2)2+4x≥2 g(x) = \begin{cases} 8 - 2x & x < 2 \\ (x - 2)^2 + 4 & x \geq 2 \end{cases} g(x)={8−2x(x−2)2+4​x<2x≥2​
a.

Find the value of gg(0)gg(0)gg(0)

[2]
b.

Find all the values of x x\,x for which g(x)>40g(x) > 40g(x)>40

[4]
c.

The function h h\,h is defined as h(x)=(x−2)2+4x≥2h(x) = (x - 2)^2 + 4 \quad x \geq 2h(x)=(x−2)2+4x≥2. Explain why h h\,h has an inverse but g g\,g does not.

[1]
d.

Solve the equation h−1(x)=2h^{-1}(x) = 2h−1(x)=2

[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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