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3.1 Algebra and functions (A-level only)

3.1 Algebra and functions (A-level only)

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Question 139

The functions fff and ggg are defined by

f(x)=12−3xfor x≤4 f(x) = \sqrt{12 - 3x} \quad \text{for } x \le 4 f(x)=12−3x​for x≤4 g(x)=1xfor x≠0 g(x) = \frac{1}{x} \quad \text{for } x \ne 0 g(x)=x1​for x=0

The function hhh has the maximum possible domain and is defined by h(x)=gf(x)h(x) = gf(x)h(x)=gf(x).

a.

Find an expression for h(x)h(x)h(x).

[1]
b.

Find the domain of hhh.

[2]
c.

Show that h−1(x)=4−13x2h^{-1}(x) = 4 - \frac{1}{3x^2}h−1(x)=4−3x21​.

[3]
Markscheme

3.1 Algebra and functions (A-level only) Questions

  1. A Level
  2. /Maths
  3. /3.1 Algebra and functions (A-level only)

281 exam-style questions on CCEA A Level Maths 3.1 Algebra and functions (A-level only), covering 3.1.1 Algebra and functions (A-level only), 3.1.2 Algebra and functions (A-level only), 3.1.3 Algebra and functions (A-level only), 3.1.4 Algebra and functions (A-level only), 3.1.5 Algebra and functions (A-level only), 3.1.6 Algebra and functions (A-level only), 3.1.7 Algebra and functions (A-level only), 3.1.8 Algebra and functions (A-level only), 3.1.9 Algebra and functions (A-level only), and 3.1 Algebra and functions (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.

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