HARD
JEE Main/Advance
IMPORTANT
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If Fx=sinπxx, then Fx is: (where . denotes fractional part function and . denotes the greatest integer function and sgnx is a signum function)

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Important Questions on Functions

HARD
JEE Main/Advance
IMPORTANT
Let f:RR and g:RR be two one-one and onto functions such that they are mirror images of each other about the line y=a. If hx=fx+gx, then hx is
HARD
JEE Main/Advance
IMPORTANT
Which of following pairs of functions are identical.
HARD
JEE Main/Advance
IMPORTANT
For the function fx=lnsin-1log2x
HARD
JEE Main/Advance
IMPORTANT
Which among the following functions defined from -1,1  to -1,1, are not bijective ?
HARD
JEE Main/Advance
IMPORTANT
Find number of all such functions y=fx which are one-one? 
HARD
JEE Main/Advance
IMPORTANT
Find the number of all such functions y=fx which are onto
HARD
JEE Main/Advance
IMPORTANT
Find the set of all solutions of the equation 2y-2y-1-1=2y-1+1.
HARD
JEE Main/Advance
IMPORTANT

Let f(x)=x2 and g(x)=sinx for all xR. Then the set of all x satisfying (fggf)(x)=(ggf)(x), where (fg)(x)=f(g(x)), is