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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 16

The function f f\,f is defined by

f(x)=(x−3)2+1f(x) = (x - 3)^2 + 1f(x)=(x−3)2+1 for x≥k x \geq k\,x≥k

where k k\,k is a constant.

a.

Given that f−1f^{-1}f−1 exists, state the least possible value of kkk.

In parts (b) to (d), k k\,k takes this least possible value.

[1]
b.

Evaluate ff(6)ff(6)ff(6).

[2]
c.

Solve the equation f(x)=xf(x) = xf(x)=x.

[3]
d.

Explain why your answer to part (c) is also the solution of the equation f(x)=f−1(x)f(x) = f^{-1}(x)f(x)=f−1(x).

[1]
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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