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Questions › JNU › JNU SSS 2017 › Q13
1 mark, −0.25Mathematics › Sets, relations and functions › Functional equations and special functionsModerateabout 2 min

JNU SSS 2017 Question 13: Sets, relations and functions

A function f(⋅)f(\cdot)f(⋅) satisfies the following two properties : (i) f(1)=1f(1) = 1f(1)=1 (ii) f(a)=(a−1)×f(a−1)f(a) = (a - 1) \times f(a - 1)f(a)=(a−1)×f(a−1) where aaa is any positive real number. Assume that nnn is a positive integer. Which one of the following statements is certainly true?

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A function f(·) satisfies the following two properties: (i) f(1) = 1 (ii) f(a) = (a - 1) × f(a - 1) where a is any positive real number. Assume that n is a positive integer. Which one of the following statements is certainly true? (A) f(n) = (n - 1) (B) f(n) = (n - 1)! (C) f(n) = n × (n - 1) (D) f(n) cannot be computed from the information given

Also written as: A function f(*) satisfies the following two properties: (i) f(1) = 1 (ii) f(a) = (a - 1) * f(a - 1) where a is any positive real number. Assume that n is a positive integer. Which one of the following statements is certainly true?

Sets, relations and functions has come up 65 times in 6 exams since 2004.

What this question tests

This question is on Functional equations and special functions, part of Sets, relations and functions in Mathematics.

Functions defined by a rule they must satisfy, or by recursion, or with unusual behaviour.

TestStop has 3 past-paper questions on this subtopic; the nearest in year are below.

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Practise Sets, relations and functionsMore on Functional equations and special functions

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Question from the JNU SSS 2017 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.