Relations and Functions Test-2 - Class 12

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CBSE TEST PAPER-02 
CLASS - XII MATHEMATICS (Relations and Functions) 
Topic:- Relation and function 
1. Prove that the function f: R 
 R, given by f(x) = 2x, is one – one. [1] 
2. State whether the function is one – one, onto or bijective f: R 
 R defined by f(x) = 1+ x
2
 [1]
3. Let S = {1, 2, 3} [1] 
Determine whether the function f: S 
 S defined as below have inverse. 
f = {(1, 2), (2, 1), (3, 1)} 
4. Find gof f(x) = |x|, g(x) = |5x + 1| [1] 
5. Let f, g and h be function from R to R show that (f + g) oh = foh = goh [1] 
6. If a * b = a + 3b
2
, then find 2 * 4 [1] 
7. Show that the relation in the set R of real no. defined R = {(a, b) : a = b
3
 }, is neither reflexive
nor symmetric nor transitive.          [4]
8. Let A = N× N and * be the binary operation on A define by (a, b) * (c, d) = (a + c, b + d)  [4]
Show that * is commutative and associative. 
9. Show that if f:
7 3
5 5
R R
? ? ? ?
- ? - ? ? ? ?
? ? ? ?
 is defining by f(x) = 
3 4
5 7
x
x
+
- and g: 
3 7
5 5
R R
? ? ? ?
- ? - ? ? ? ?
? ? ? ?
is 
define by g(x) = 
7 4
,
5 3
x
x
+
- then fog = I A and gof = I B  when 
3 7
,  
5 5
A R B R
? ? ? ?
= - = - ? ? ? ?
? ? ? ?
; I A (x) = x, 
for all x?A, I B(x) = x, for all x?B are called identify function on set A and B respectively. [4]
10. Let f: N  
 N be defined by f(x) = 
1
,     all n
2
   
2
n
if n is odd for N
n
if n is even
+ ? ?
?
? ?
? ?
? ?
? ?
? ?
? ?
Examine wether the function 
f is onto, one – one or bijective [4]