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1.3 Functions

1.3 Functions

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Question 12

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

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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