Consider the set of integers from to

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Consider the set Z5={−5,−4,…,0,…,4,5}\mathbb Z_{5}=\{-5,-4,\dots,0,\dots,4,5\} of integers from −5-5 to 55. A relation TT on Z5\mathbb Z_{5} is defined by T={(x,y)∣y2=25−x2,  x,y∈Z5}.T=\{(x,y)\mid y^{2}=25-x^{2},\;x, y\in\mathbb Z_{5}\}. (i) For x=0,1,2x=0,1,2 list all corresponding values of yy that belong to TT. (ii) Is TT a function from Z5\mathbb Z_{5} to Z5\mathbb Z_{5}? Give a clear reason based on the outputs obtained in part (i) and on the defining rule. (iii) Suggest a restriction on the domain or the range (state it explicitly) that converts TT into a function, and justify why the restricted relation satisfies the definition of a function.

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