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Questions › DSE › DSE 2011 › Q22
2 marksMathematics › Sets, relations and functions › Functional equations and special functionsModerateabout 3 min

DSE 2011 Question 22: Sets, relations and functions

Suppose a real valued function fff is defined for all real numbers excepting 0, and satisfies the following condition: f(xy)=f(x)+f(y)f(xy)=f(x)+f(y)f(xy)=f(x)+f(y) for all x,yx,yx,y in the domain. Consider the statements: (i) f(1)=f(−1)=0f(1)=f(-1)=0f(1)=f(−1)=0; (ii) f(x)=f(−x)f(x)=f(-x)f(x)=f(−x) for every xxx.

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Suppose a real valued function f is defined for all real numbers excepting 0, and satisfies the following condition: f(xy)=f(x)+f(y) for all x,y in the domain. Consider the statements: (i) f(1)=f(-1)=0; (ii) f(x)=f(-x) for every x. (A) (i) is true and (ii) is false. (B) (i) is false and (ii) is true. (C) Both are true. (D) Both are false.

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 DSE 2011 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.