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Let A be a non- empty set of real number...

Let A be a non- empty set of real numbers and `f:A->A` be such that `f(f(x))=x AA x in R` then f(x) is (A) bijection (B) one-one but not onto (C) onto but not one-one (D) neither one-one nor onto

A

a bijection

B

one-one but not onto

C

onto but not one-one

D

neither one-one nor onto

Text Solution

Verified by Experts

The correct Answer is:
A
`x, y in A` and `f(x)=f(y) rArr f(f(x))= f(f(y))`. So, f is one-one
Also `a in A rArr f(f(a))=arArr f(b)=a` where `b=f(a) in A`. So, f is onto.
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