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1.3 Functions

1.3 Functions

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Question 80

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

1.3 Functions Questions

  1. A Level
  2. /Maths
  3. /1.3 Functions

181 exam-style questions on OCR (MEI) A Level Maths 1.3 Functions, covering 1.3.1 Operations on polynomials, 1.3.2 Factor theorem, 1.3.3 Definition of a function (A-level only), 1.3.4 Composite functions (A-level only), 1.3.5 Inverse functions and their graphs (A-level only), 1.3.6 The modulus function (A-level only), 1.3.7 Inequalities with a modulus sign (A-level only), and 1.3.8 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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