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)
= x2
(ii) f: Z → Z given by f(x)
= x2
(iii) f: R → R given by f(x)
= x2
(iv) f: N → N given by f(x)
= x3
(v) f: Z → Z given by f(x)
= x3
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 + x2
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) = x4. 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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