Ex 1.3, 11 - Consider f: {1, 2, 3} -> {a, b, c}, f(1) = a - Finding Inverse

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  1. Chapter 1 Class 12 Relation and Functions
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Ex 1.3, 11 Consider  𝑓 : {1, 2, 3} → {a, b, c} given by  𝑓(1) = a,  𝑓(2) = b and  𝑓(3) = c. Find ﷐𝑓﷮−1﷯ and show that ﷐﷐﷐𝑓﷮−1﷯﷯﷮−1﷯  =  𝑓. 𝑓 : {1, 2, 3} → {a, b, c} is given by, 𝑓(1) = a,  𝑓(2) = b, and  𝑓(3) = c Finding ﷐𝒇﷮−𝟏﷯ So, 𝑓 = {(1, a) ,(2, b) ,(3, c)} ﷐𝒇﷮−𝟏﷯ = {(a, 1) ,(b, 2) ,(c, 3)} Hence, ﷐𝒇﷮−𝟏﷯ (a) = 1, ﷐𝒇﷮−𝟏﷯(b) = 2, and ﷐𝒇﷮−𝟏﷯(c) = 3 Now, ﷐𝑓﷮−1﷯ = {(a, 1) ,(b, 2) ,(c, 3)} ﷐﷐﷐𝒇﷮−𝟏﷯﷯﷮−𝟏﷯ = {(1, a) ,(2, b) ,(3, c)} = 𝑓 Hence, ﷐﷐﷐𝑓﷮−1﷯﷯﷮−1﷯ = 𝑓

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