Consider f- 1- 2- 3-a- b- c given by f1 - a- f2 - b and f3 - c- Find f-1 and show that f-1-1 - f

f^ 1 : (a,b,c)→ (1,2,3) f(a)=1,f(b)=2,f(c)=3 Now, (f^ 1)^ 1 : (1,2,3) →(a,b,c) = f ...

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Standard XII

Mathematics

Definition of Functions

Consider f:...

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 $(f^{- 1})^{- 1} = f$

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Solution

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

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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:(a,b,c)→(1,2,3)f(a)=1,f(b)=2,f(c)=3Now,(f−1)−1:(1,2,3)→(a,b,c)=f

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 $(f^{- 1})^{- 1} = f$

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