MEDIUM
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Let f:R+R+ be a mapping define by fx=x3+4. Then f is

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Important Questions on Relations and Functions

HARD
For a real number r let r denote the largest integer less than or equal to r. Let a>1 a real number which is not an integer and k be the smallest positive integer such that ak>ak Then which of the following statement is always true?
MEDIUM
The function f :R-12,12 defined as fx=x1+x2, is:
HARD
For a real number r we denote by r the largest integer less than or equal to r. If x, y are real numbers with x, y 1 then which of the following statements is always true?
HARD
If [x] denotes the greatest integer x, then the system of linear equations [sinθ]x+[-cosθ]y=0[cotθ]x+y=0
MEDIUM
Show that the function f:NN defined by fn=n+1 is not onto, by drawing arrow diagrams.
MEDIUM
If the function f:R-1, -1A defined by fx=x21-x2, is surjective, then A is equal to
HARD
The function f :NI defined by fx=x-5x5 , where N is the set of natural numbers and x denotes the greatest integer less than or equal to x, is:
EASY
Let A=  { xR:x is not a positive integer} . Define a function  f:AR as fx=2xx-1 , then f is:
HARD
If a ∈ R  and the equation -3(x - [x])2+2(x - [x])+a2 = 0 (where [x] denotes the greatest integer  x) has no integral solution, then all possible values of a lie in the interval 
HARD
For xR,  Let [x] denotes the greatest integer x, then the sum of the series -13+-13-1100+-13-2100+.....+-13-99100 is
EASY
Which of the following function from z into z is bijection? (z is set of integers)
MEDIUM
Let f and g be differentiable functions on R such that fog is the identity function. If for some a, bR, g'a=5 and ga=b, then f'b is equal to:
HARD
Let f: RR be defined by fx=x-1x+1, then f is 
MEDIUM
If A={x|xN,x5},B=x|xZ,x2-5x+6=0, then the number of onto functions from A to B is
MEDIUM
Let A={a,b,c} and B={1,2,3,4}. Then the number of elements in the set C={f:AB2f(A) and f is not one-one} is
MEDIUM
Let t denote the greatest integert. Then the equation in x, x2+2x+2-7=0 has :
HARD

Let R be the set of real numbers and f:RR be defined by fx=x1+x2, where x is the greatest integer less than or equal to x, and x=x-x. Which of the following statement are true?

I. The range of f is closed interval
II. f is continuous on R
III. f is one-one on R

MEDIUM
Show that the function f:RR defined by fx=xx2+1,x is neither one-one nor onto. Also, if g:RR is defined as g(x)=2 x-1, find fog(x).
EASY
Let f:RR be defined as f(x)=3x. Then