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1.3 Functions

1.3 Functions

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Question 3
35%

The functions f f\,f and g g\,g are defined by

f:x→ln⁡(2x−1),x∈R,x>12 f: x \rightarrow \ln(2x - 1), \quad x \in \mathbb{R}, x > \frac{1}{2} f:x→ln(2x−1),x∈R,x>21​ g:x→4x−1,x∈R,x≠1 g: x \rightarrow \frac{4}{x-1}, \quad x \in \mathbb{R}, x \neq 1 g:x→x−14​,x∈R,x=1
a.

Find the exact value of fg(3)fg(3)fg(3)

[2]
b.

Find an expression for f−1(x)f^{-1}(x)f−1(x) and state its domain

[4]
c.

Sketch the graphs of f(x)f(x)f(x) and f−1(x)f^{-1}(x)f−1(x) on the same diagram

[3]
d.

Sketch the graph of y=∣g(x)∣y = |g(x)|y=∣g(x)∣

[3]
e.

Find the exact values of ∣4x−1∣=2\displaystyle | \frac{4}{x-1} | = 2∣x−14​∣=2

[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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