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Function - Assignment 2

The document contains a series of mathematical problems and their solutions, including inequalities, domain definitions, and injective functions. It lists specific equations to solve and provides answers to each problem. The answers include intervals and conditions for the solutions, as well as evaluations of function properties.

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18 views2 pages

Function - Assignment 2

The document contains a series of mathematical problems and their solutions, including inequalities, domain definitions, and injective functions. It lists specific equations to solve and provides answers to each problem. The answers include intervals and conditions for the solutions, as well as evaluations of function properties.

Uploaded by

souravroy.sr5989
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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PRE-RMO MATHEMATICS FUNCTION

1
1. Solve  1 where x  R, x   2
x 2
2. Solve x  1  x  1  0
3. Solve for x: 2  x  3  4
Solve for x: x  3 x  2  0
2
4.
5. Solve for x: 2  x  2  1

x 4
2

6. Solve for x: 0
x 1
1
7. Solve for x: 2
x3
x2  2
8. Solve for x: 1
3x
1
9. Find domain :- y 
x 5

10. Solve for x: x  1  x  3  5


11. Solve for x: 2 x  1  x  2  5
12. Is the following function is injective map?
f  x   x  2 , x [2, )
13. Is the following function is injective map?
f  x   x x , x   ,  
1 
x
14. The domain of definition of f  x   is
2 
x
(a)  , ∞    2,2 (b)  , ∞    1,1

(c)  1,1   ∞, 2    2, ∞  (d) None of the above


1
15. The domain of the function f defined by f ( x)  is
x | x |
(a) R (b) R+ (c) R- (d) None of these
ANSWERS KEY

1.  2, 1  1, 2  2. No solution 3. 1  x  1 or 5  x  7

4.  x  ( , 2]  [1,1]  [2,  ) 5. x  1,3 6. No solution

8. x  1, 2
5 7
7. x  or x  9. x  R  5
2 2
 1   9 4 
10. x    ,1  1,3  3,  11. x   , 2    ,   12. Yes
2   2 3 
13. Yes 14. C 15. d

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