{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.
Answer:
Given
f : {1, 2, 3} 
{a,
b, c}
for
distinct values of x in {1, 2, 3}, there are distinct values of y in {a,
b, c}.
is onto.
Hence
f is both one-one and onto.
is
invertible.
and
Now
for distinct values of x in {a, b, c}, there are distinct values of y in {1, 2,
3}
is one-one.
Also
for every 
there exists
a unique element 
is onto.
Hence
f?1 is both one-one and onto.
is
invertible.
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