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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 11

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

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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