#### ElitmusZone

ElitmusZone » Functions

# Functions

 01. If  f(x)=| x – 2 |,  then which of the following is always true ? (a) f(x) = (f(x))2 (b) f(x) = f(-x) (c) f(x) = x – 2 (d) None of these
 02. Which of the following functions will have a minimum value at x = -3 ? (a)f(x) = 2x3 – 4x + 3 (b)  f(x)=4x4– 3x+5 (c)  f(x) = x6 – 2x – 6 (d) None of these
 03. Find the maximum value of the functions 1/(x2 – 3x + 2) ? (a) 11/4 (b) 1/4 (c) 0 (d) None of these
 04. Find the minimum value off function f(x)= log(x2 – 2x + 5) (base 2) ? (a) -4 (b) 2 (c) 4 (d) -2
 05. A function f(x) satisfies f(1)=3600  and f(1) + f(2) +……f(n) =n2f(n), for all positive integers n>1. What is the value of f(9) ? (a) 200 (b) 100 (c) 120 (d) 80
 06. Let f(x)= max( 2x + 1, 3 – 4x), where x is any real number. Then, the minimum possible value of f(x) is (a) 4/3 (b) 1/2 (c) 2/3 (d) 5/3
 07. Let g(x) be a function such that g(x + 1) + g(x – 1) = g(x) for every real x. Then, for what value of p is the relation g(x + p)= g(x) necessarily true for every real x ? (a) 5 (b) 3 (c) 2 (d) 6
 08. If f(x)=x3– 4x + p  and f(0) and f(1) are of opposite signs, then which of the following is necessarily true ? (a) -1 < p < 2 (b) 0 < p < 3 (c)  -2 < p < 1 (d) -3 < p < 0
 09. Let g(x) =  max ( 5 – x , x + 2 ). The smallest possible value of g(x) is ? (a) 4.0 (b) 4.5 (c) 1.5 (d) None of these
 10. Let f(x)= |x – 2| + |2.5 – x| + |3.6 – x|, where x is a real number, attains a minimum at ? (a) x = 2.3 (b) x = 2.5 (c) x = 2.7 (d) None of these
 11. Largest value of min ( 2 + x2 , 6 – 3x), when x > 0 is (a) 1 (b) 2 (c) 3 (d) 4

 1 D 2. D 3 D 4. B 5 D 6. D 7 D 8. B 9 D 10. B 11 C

Detailed Solution

1. ankit jain

Contents fulfil the need of Elitmus’s exam……….Thanks for providing it…….great stufff

2. Rajat Tripathi

f(1) = 3600
3600 + f(2)= 4f(2)–>f(2)= 1200
4800 + f(3)= 9f(3)–>f(3)= 600
5400 + f(4)= 16f(4)–>f(4)= 360
5760 + f(5)= 25f(5)–>f(5)= 240
6000 + f(6)= 36f(6)–>f(6)= 171.428
6171.428 + f(7)= 49f(7)–> f(7)=128.571
6300 + f(8)=64f(8)–>f(8)= 100
6400 + f(9)= 81f(9)–>f(9)= 80

3. Jasvinder Singh

answer for Q.3 should be d.
to get max. value denominator should be min. and min. value can be calculated by putting x=-b/2a