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Questions › DSE › DSE 2009 › Q27
2 marksMathematics › Sets, relations and functions › Functions: domain, range and compositionModerateabout 3 min

DSE 2009 Question 27: Sets, relations and functions

A function f(x1,x2,T)=(y1,y2)f(x_{1},x_{2},T)=(y_{1},y_{2})f(x1​,x2​,T)=(y1​,y2​) is defined as follows, where x1,x2,Tx_{1},x_{2},Tx1​,x2​,T are non-negative reals and x1+x2≥Tx_{1}+x_{2}\ge Tx1​+x2​≥T: y1=min⁡(α,x1)y_{1}=\min(\alpha,x_{1})y1​=min(α,x1​), y2=min⁡(α,x2)y_{2}=\min(\alpha,x_{2})y2​=min(α,x2​) such that y1+y2=Ty_{1}+y_{2}=Ty1​+y2​=T. Find f(5,2,6)f(5,2,6)f(5,2,6).

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A function f(x₁,x₂,T)=(y₁,y₂) is defined as follows, where x₁,x₂,T are non-negative reals and x₁+x₂≥ T: y₁=min (α,x₁), y₂=min (α,x₂) such that y₁+y₂=T. Find f(5,2,6). (A) (3,3) (B) (5,1) (C) (0,6) (D) (4,2)

Also written as: A function f(x_1,x_2,T)=(y_1,y_2) is defined as follows, where x_1,x_2,T are non-negative reals and x_1+x_2>= T: y_1=min (alpha,x_1), y_2=min (alpha,x_2) such that y_1+y_2=T. Find f(5,2,6).

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

What this question tests

This question is on Functions: domain, range and composition, part of Sets, relations and functions in Mathematics.

What makes a rule a function, its domain and range, composition and graph transformations.

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Question from the DSE 2009 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.