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**CBSE Guide NCERT
Solutions for Class 12 Mathematics **

**Chapter 1, relations and functions**

*(*

__Solutions of CBSE Class 12 NCERT Maths Exercise 1.2, Relations and Functions__)**Scroll down and click on the Link in between & at the end of Questions to open Solutions (pdf)**

Question 1: Show
that the function

*f*: R* → R* defined by f(x) = 1/x is one-one and onto, where R* is the set of all non-zero real numbers. Is the result true, if the domain R* is replaced by N with co-domain being same as R*?
Question 2: Check
the injectivity and surjectivity of the following functions:

(i)

*f*: N → N given by*f*(*x*) =*x*^{2}
(ii)

*f*: Z → Z given by*f*(*x*) =*x*^{2}
(iii)

*f*: R → R given by*f*(*x*) =*x*^{2}
(iv)

*f*: N → N given by*f*(*x*) =*x*^{3}
(v)

*f*: Z → Z given by*f*(*x*) =*x*^{3}
Question 3: Prove
that the Greatest Integer Function

*f*: R → R given by*f*(*x*) = [*x*], is neither one - one nor onto, where [*x*] denotes the greatest integer less than or equal to*x*.

**Class XII CBSE Maths - NCERT Solutions of Relations and Functions Ex 1.2**
Question 4: Show
that the Modulus Function f: R → R given by, is neither one-one nor onto, where
|x| is x, if x is positive or 0 and |x| is − x, if x is negative.

Question 5: Show
that the Signum Function f: R → R, given by

is
neither one-one nor onto.

Question 6: Let
A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a
function from A to B. Show that f is one-one.

Question 7: In
each of the following cases, state whether the function is one-one, onto or
bijective.

Justify
your answer.

(i)
f: R → R defined by f(x) = 3 − 4x

(ii)
f: R → R defined by f(x) = 1 + x

^{2 }
Question 8: Let

*A*and*B*be sets. Show that*f*:*A*×*B*→*B*×*A*such that (*a*,*b*) = (*b*,*a*) is bijective function.

**Relations and Functions - Class 12 Mathematics CBSE Guide NCERT Solutions**

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Question 9:

Question 10: Let
A = R − {3} and B = R − {1}. Consider the function f: A → B defined by

Is
f one-one and onto? Justify your answer.

Question 11: Let
f: R → R be defined as f(x) = x

^{4}. Choose the correct answer.
(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

Question 12: Let
f: R → R be defined as f(x) = 3x. Choose the correct answer.

(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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