CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 2 – Relations and Functions Maths
______________________________________________________________________________
Thus, it can be clearly observed that the range of f is the set of all real numbers greater than 2.
i.e., range of
f
2,
Alter:
Let x be any real number. Accordingly,
2
x 0
2
x
2
x
f
2 0 2
2 2
x 2
Range of
(iii)
,
f
f x x x
2,
is a real number
It is clear that the range of f is the set of all real numbers.
.
Range of
f R
Miscellaneous Exercise
Question 1:
The relation f is defined by
f
x
x
2 , 0 x3
3 x, 3 x10
x
2 , 0 x2
The relation g is defined by g x
x x
Show that f is a function and g is not a function.
Solution 1:
The relation f is defined as
f
x
x
2 , 0 x3
3 x, 3 x10
It is observed that for
0 x 3, f x x
3 x 10, f x 3x
2
3 , 2 10
2
Also, at x 3, f x 3 9 or f x 33 9 i.e., at x f x
Therefore, for 0 x 10
, the images of f
3, 9
x are unique. Thus, the given relation is a function.
Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a
Top tutor.