Relation and Function
NCERT Exemplar Problem
Long Answer Type Part 2
Question 20: Let A = R – {3}, B = R – {1}. Let
be defined by
Then show that f is bijective.
Solution: Given,
Now, for injectivity:
After cross multiplication, we get
Thus, f(x) is an injective function.
Now, for surjectivity:
Therefore, f(x) is a surjective function.
Here, we can see that f(x) is a surjective and injective both funtion.
Thus, f(x) is bijective.
Question 21: Let A = [– 1, 1]. Then, discuss whether the following functions defined on A are one-one, onto or bijective:
Solution:
This shows that f(x) is one-one
Clearly, f(x) is not onto.
Thus, f(x) is not bijective as it is one-one and not onto.
Solution:
Clearly, g(x) is not one-one
Here, it is also clear that g(x) is not onto.
Since, g(x) is neither one-one nor onto, thus g(x) is not bijective.
Solution:
Hence, h(x) is a surjective function.
There h(x) is bijective.
Solution:
Here, it is clear that k(x) is not one-one.
