Relation and Function
NCERT Exemplar Problem
Long Answer Type Part 4
Question 25: Functions
are defined respectively, by
find:
(i) fog
Solution:
(ii) gof
Solution:
(iii) fof
Solution:
(iv) gog
Solution:
Question: 26 – Let * be the binary operation defined on Q. Find which of the following binary operations are commutative.
Solution:
Question: 27 – Let * be binary operation defined on R by
Then the operation is:
(i) Commutative but not associative
(ii) associative but not commutative
(iii) neither commutative nor associative
(iv) both commutative and associative.
Answer: (i) is commutative but not associative.
Explanation:
Therefore, * is commutative.
Now, from equation (i) and (ii) it is clear that
