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 if ( f - 1 ) - 1 = f.

f = (1, a), (2, 6), (3, c) . Clearly/is one-one and onto. Also, f - 1 = (0, 4), (6, 2), (c, 3) (a) = 1, f - 1 (b) = 2, f - 1 (c) = 3 Also, ( f - 1 ) 1 = (1,a),(2,b),(3,c) = f Hence, the result ( f - 1 ) - 1 = f .

Relations and Functions — Class 12 Maths Solution

ncert exercise SA NCERT Ex. 1.3,Q.11, Page 19

Question

Consider f : $\{1, 2, 3\} \to \{a,b,c\}$ given by $f(1) = a,f(2) = b$ and $f(3) = c.$ Find ${f^{ - 1}}$ and show that if ${({f^{ - 1}})^{ - 1}} = f.$

Step-by-step Solution

f$= \{(1, a), (2, 6), (3, c)\}$. Clearly/is one-one and onto.

Also, ${f^{ - 1}} = \{(0, 4), (6, 2), (c, 3)\}$

$\Rightarrow$ ${f^{ - 1}}(a) = 1,{f^{ - 1}}(b) = 2,{f^{ - 1}}(c) = 3$

Also, ${({f^{ - 1}})^1} = \{ (1,a),(2,b),(3,c)\} = f$

Hence, the result ${({f^{ - 1}})^{ - 1}} = f$ .

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