Functions Question 568
If X and Y are two non-empty sets where $ f:X\to Y $ is a function defined such that $ f(C)={ f(x):x\in C } $ for $ C\subseteq X $ and $ {f^{-1}}(D)={x:f(x)\in D} $ for $ D\subseteq Y $ for any $ A\subseteq X $ and $ B\subseteq Y, $ then
[IIT Screening 2005]
Options:
A) $ {f^{-1}}(f(A))=A $
B) $ {f^{-1}}(f(A))=A $ only if $ f $ is bijective
C) $ f({f^{-1}}(B))=B $ only if $ B\subseteq f(X) $
D) $ f({f^{-1}}(B))=B $
Show Answer
Answer:
Correct Answer: C
Solution:
The set B satisfied the above definition of function f so option is correct.
BETA
