Page 17 - Mathematics Class - XII

Viva-Voce

1. What is one-one function?
Ans. A function f is one-one, if every element of the range of the function f corresponds to exactly one element
of the domain of f.

2. What is injective function?
Ans. One-one function is also known as injective function.
3. What is surjective function?

Ans. Onto function is also called surjective function which means that every element of B has at least one
(or more) matching element in A. There won't be any element of B left out.
4. What is bijective function?

Ans. Bijective means a function which is both injective and surjective together.
In bijective function there is perfect “one-to-one correspondence” between the elements of the sets.
If every element of A goes to a unique element of B, and every element of B has a matching in A.

5. If f : A → B is a bijective function, such that n(A) = 8, then n(B) = ?
Ans. We know that a bijective function is one-one and onto function. So, range of f = Co domain of f

∴ n(A) = n(B) = 8.

MCQs

1. Function f : N → N defined by f (x) = x – 1 for f (1) = f (2) = 1 and x > 2 is
a) one-one and onto b) onto but not one-one

c) Neither one-one nor onto d) None of these

2. Let f : R → R be defined as f (x) = x . Choose the correct one.
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a) f is one-one onto b) f is many-one onto

c) f is one-one not onto d) f is neither one-one nor onto
3. Let f : R → R be defined as f (x) = 3x. Choose the correct one

a) f is one-one onto b) f is many-one onto
c) f is one-one but not onto d) f is neither one-one nor onto

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4. Let f : R → R defined as f (x) = , ∀ x ∈ R, then f is
x
a) one-one b) onto c) one-one onto d) None of these

Answers: 1. b) onto but not one-one 2. d) f is neither one-one nor onto
3. a) f is one-one onto 4. c) one-one onto

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