1.
The domain of the function f ( x ) = n ( )
x 2 − 5 x − 24 − x − 2 is:
(a) ( −, −3 (b) ( −, −3 8, )
−28
(c) −, (d) None of these
9
3x − 4 x
2. Domain of definition of the function f ( x ) =
x 2 − 3x − 4
(a) ( −,0 (b) 0, )
(c) ( −, −1) 0,4) (d) ( −,1) (1,4)
+ log( 2x−5) ( x 2 − 3x + 10 ) +
1 1
3. The number of integers lying in the domain of f ( x ) =
x 1− | x |
(a) 0 (b) 3
(c) 4 (d) Infinite
( )
−1/2
4. If f ( x ) = x12 − x9 + x4 − x + 1 the value of x satisfies
(a) (1,) (b) ( −, −1)
(c) ( −1,1) (d) 1, −1
5. Domain of f ( x ) is ( 0,1) implies the complete set of domain of f ( e x ) + f ( n | x |) is ( a, b ) , then what is the
value of 1 + e + a + b .
x 2 + 14 x + 9
6. Range of the function y = ,xR
x2 + 2 x + 3
(a) ( −5,4) (b) −5,4
(c) ( −, −5) ( 4, ) (d) −1,1
7. The number of real roots of the equation 3| x| ( 2− | x |) = 1 is:
(a) 1 (b) 2
(c) 3 (d) 4
Find domain f ( x ) = x − 5 + 10 − x
2 2
8.
2 x2 − 5x + 3
9. The range of value of for which the expression can take all real values for x R − is
4x − 4
(a) ( 4,6) (b) 4,6
(c) (4, 6] (d) [4, 6)
10. The function f ( x ) = 2 | x | + | x + 1| − | x − 3| −3| x | has a local minimum or a local maximum at x =
3
(a) 0 (b) −
2
3
(c) (d) 3
4
2
x x
11. If 2 + 2 + k 0 for all real x , then find sum of modulus of all integral values of k in
x − 5x + 9 x − 5x + 9
−4,7
12. Range of the function y = x8 + x 6 + 4 x 2 + 7
13. Find range: y = x ( x + 2)( x + 4)( x + 6) + 5
1
14. Range of y = x 2 + x + 2 +
x2 + x + 2
x2 + 5x − 6
15. Range of y =
x 2 − 36
