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Which of the following relations are functions? Give reasons. In case of a function, find its domain and range. (i) `f={(1 ,3),(1,5),(2,3),(2,5)}` (ii) `g={(2,1),(5,1),(8,1),(11,1)}` (iii) `h={(2,1),(4,2),(6,3),(8,4),(10,5),(12,6)}` |
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Answer» (i) `f={(1,3),(1,5),(2,3),(2,5)}` Here, one element, namely 1 has two images 3 and 5 under f. `:.` f is not a function. (ii) `g={(2,1),(5,1),(8,1),(11,1)}`. Clearly, no two distinct ordered pairs in g have the same first coordinate. So, g is a function. `:.` dom (g)=[2,5,8,11] and range `g={1}`. (iii) `h={(2,1),(4,2),(6,3),(8,4),(10,5),(12,6)}`. Cleardinate, no two distinct ordered pairs in h have the same first coordinate. So, h is a function. `:.` dom `(h)={2,4,6,8,10,12}` and range `(h)={1,2,3,4,5,6}`. |
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