HARD
Mathematics
IMPORTANT
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The function fx=cos-12[|sinx|+|cosx|]sin2x+2sinx+114 is defined if x belongs to (where · represents the greatest integer function):

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Important Questions on Functions

HARD
Mathematics
IMPORTANT
Consider a function fx=sgnx+sgnx+sgnx defined in the interval -5,5, where  ·and · represent the greatest integer and the fractional part functions respectively. Then
HARD
Mathematics
IMPORTANT
If nf1x,f2x denotes the number of solutions of the equation f1x=f2x, then which of the following is/are CORRECT?
HARD
Mathematics
IMPORTANT
Suppose that f:RR is continuous and satisfying the equation fx·ffx=1, for all real x. Let f1000=999, then which of the following is/are true?
HARD
Mathematics
IMPORTANT
Let fx be a real-valued function such that f0=12 and fx+y=fxfa-y+fyfa-x  x, yR, then for some real a:
HARD
Mathematics
IMPORTANT
If a function satisfies x-yfx+y-x+yfx-y=2x2y-y3  x, yR and f1=2, then
HARD
Mathematics
IMPORTANT
The function g defined by g(x)=sinsin-1{x}+cossin-1{x}-1 (where {x} denotes the functional part function) is:
HARD
Mathematics
IMPORTANT
If Fx=sinπxx, then Fx is: (where . denotes fractional part function and . denotes the greatest integer function and sgnx is a signum function)
HARD
Mathematics
IMPORTANT

If the value of x (non-integer) satisfying the equation x+92x=x+92x is m, then find m.

Where · denotes the greatest integer function.