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1.3 Functions

1.3 Functions

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Question 111

The cooling efficiency, EEE, of a high-performance server rack is modelled by the function

E(v)=5v−2v−4,v>4 E(v) = \frac{5v - 2}{v - 4}, \quad v > 4 E(v)=v−45v−2​,v>4

where v v\,v is the coolant flow rate in litres per minute.

a.

Use differentiation to show that E E\,E is a decreasing function on its domain.

[3]
b.

Find an expression for E−1(v)E^{-1}(v)E−1(v) and state its domain.

[4]
ci.

Show that the composite function EE(v)EE(v)EE(v) can be written in the form av+bv+c\displaystyle \frac{av + b}{v + c}v+cav+b​, where a,b, a, b,\,a,b, and c c\,c are integers to be found.

[3]
cii.

Deduce the range of EEEEEE.

[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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