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TitleFunction ASSIGNMENT FOR IIT-JEE
TagsFunction (Mathematics) Sine Mathematical Analysis Mathematical Concepts Functions And Mappings
File Size1.4 MB
Total Pages13
Document Text Contents
Page 1

1. The period of the function, f(x) = [sin 3x] + |cos 6x| is : ( [.] denotes the greatest integer less than or equal to x)

(a) π (b)
3


(c) 2π (d)

2

π

2. The function f(x) =
[ ]

sec−



1 x

x x
, where [x] denotes the greatest integer less than or equal to x is defined for all

x belonging to :

(a) R (b) R - {(-1, 1) ∪ {n : n ∈ I)} (c) R′ - (0, 1) (d) R′ - {n : n ∈N}

3. The function f(x) = )x(log 2x is defined for x belonging to :

(a) (- ∞ , 0) (b) (1,∞ ) (c) (0, ∞ ) (d) none of these

4. If f(x) = ,1
4

5
gand

3
xcos.xcos

3
xsinxsin 22 =














 π++






 π++ then (gof)(x) =

(a) 1 (b) -1 (c) x (d) none of these

5. Let [x] denote the greatest integer x≤ . The domain of definition of function
2]x[

x4
)x(f

2

+


= is

(a) ]2,1[)2,( −∪−−∞ (b) [0, 2] (c) [-1, 2] (d) (0, 2)

6. The domain of definition of the function 






 −
=

4

xx5
log)x(f

2

10 is

(a) [1, 4] (b) (1, 4) (c) (0, 5) (d) [0, 5]

7. The range of the function
x3cos2

1
)x(f


= is

(a) 



− 0,

3

1
(b) R (c) 





1,
3

1
(d) none of these

8. The domain of definition of the function
x|x|

1
)x(f


= is

(a) R (b) (0,∞ ) (c) (-∞ ,0) (d) none of these

LEVEL - 1 (Objective)

FUNCTION

Page 6

12. If ),2[),1[:f ∞→∞ is given by
x

1
x)x(f += then find )x(f 1− . (assume bijective).

13. Let ),4/3[),2/1[:f ∞→∞ , where f(x) = x2 - x + 1. Find the inverse of f(x).

14. ,
x]x[

1
)x(f


= where [ ] denotes greatest integral function less than or equals to x. Then find domain of f(x).

15. Find the domain of
)13x7x(log

1
)x(f

2
2/1 +−

=

16. Find the domain of single valued function y = f(x) given by the equation 10x + 10y = 10.

17. Let 





 π∈

2
,0x , then find the solution of the function

xtanlog

1
)x(f

xsin−
= .

18. Find the range of log
3
(log

1/2
(x2 + 4x + 4)).

19. Find the domain & range of : 2
2

x
9

sin3)x(f −
π

= .

20. Find the inverse of following functions:

(i) ]3,3[x),3/x(sin)x(f 1 −∈= − [assuming bijective]

(ii) ]3,1[x),1x3x(ln)x(f 2 ∈++= . [assuming bijective]

21.




≤≤
≤≤−−

=
1x0,x

0x1,1x
)x(f

2
and g(x) = sinx. Find h(x) = f(|g(x)|) + |f(g(x))|.

22. If ,x]cos[x]cos[)x(f 22 π−+π= where [x] stands for the greatest integer function, then evaluate

)4/(fand)(f),(f),2/(f ππ−ππ .

23. A cubic expression f(x) satisfies the condition 





=






+

x

1
f)x(f

x

1
f)x(f , then prove that f(x) = 1 + x3or1 - x3.

If f(3) = 28. Then prove that f(2) = 9.

24. Let f(x) be a polynomial function satisfying, Ry,x2)xy(f)y(f)x(f)y(f)x(f ∈∀−++= . If f(2) = 5 then
prove that f(5) = 26.

25. If for non-zero x, 5
x

1

x

1
bf)x(af −=






+ where ba ≠ then find f(x).

Page 7

1. The domain of the function 1x)x1log()x(f 2 −+−= is

(a) [-1, 1] (b) ),1( ∞ (c) (0, 1) (d) ]1,( −−∞

2. The range of the function 2

2

x

x1
)x(f

+
= is equal to

(a) [0, 1] (b) (0, 1) (c) ),1( ∞ (d) ),1[ ∞

3. The curves 2x3xyand2|x|3|x|y 2323 ++=++= have the same graph for

(a) x > 0 (b) 0x ≥ (c) all x except 0 (d) all x

4. Domain of the function 7
3x

1
2

x

1
)x(f xsin

2

1

+


++=


is

(a) φ (b) R - {0} (c) R (d) None of these

5. The domain of definition of the function )1x(loge3y 1x
2

−= − is

(a) ),1( ∞ (b) ),1[ ∞ (c) R ~ {1} (d) ),1()1,( ∞∪−−∞

6. The range of the function f(x) = cos [x], where
2

x
2

π
<<

π
− , is

(a) {-1, 1, 0} (b) {cos 1, 1, cos 2} (c) }1,1cos,1{cos − (d) none of these

7. If b2 - 4ac = 0 and a > 0, then domain of the function y = log (ax3 + (a + b)x2 + (b + c)x + c) is

(a)









a2

b
~R

2

(b) 







−≥∪






− }1x|x{

a2

b
~R

(c) 







−−∞∪






− ]1,(

a2

b
~R (d) none of these

8. Which of the following functions is an even function?

(a) xx

xx

aa

aa
)x(f −




+

= (b)
1a

1a
)x(f

x

x


+

= (c)
1a

1a
x)x(f

x

x

+


= (d) ( )1xxlog)x(f 22 ++=
9. If (log

3
x) (log

x
2x) (log

2x
y) = log

x
x2, then y is equal to

(a) 9 (b) 18 (c) 27 (d) 81

LEVEL - 3
(Questions asked from previous Engineering Exams)

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