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1.1 OT1: Mathematical argument, language and proof

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12
Question 1

The function fff is defined by

f(x)=xx−5 f(x) = \frac{\sqrt{x}}{x - 5} f(x)=x−5x​​

where fff has its maximum possible domain.

a.

Find the domain of fff. Give your answer using set notation.

[2]
b.

Bob correctly calculates f(4)=−2f(4) = -2f(4)=−2 and f(9)=0.75f(9) = 0.75f(9)=0.75. He argues that because there is a change of sign, there must be a value of xxx in the interval 4<x<94 < x < 94<x<9 such that f(x)=0f(x) = 0f(x)=0. Explain the error in Bob's argument.

[2]
c.

By considering any turning points of fff, determine whether fff has an inverse function. Fully justify your answer.

[5]
Markscheme

1.1 OT1: Mathematical argument, language and proof Questions

  1. A Level
  2. /Maths
  3. /1.1 OT1: Mathematical argument, language and proof

7 exam-style questions on AQA A Level Maths 1.1 OT1: Mathematical argument, language and proof, covering 1.1.1 Constructing mathematical arguments, 1.1.2 Mathematical language and syntax, 1.1.3 Set theory language and symbols, 1.1.4 Definition, domain and range of functions, and 1.1.5 Comprehending and critiquing arguments. Each one has a worked solution and a mark scheme showing where the marks go.

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