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Mathematics
IMPORTANT
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If F(x) and G(x) are even and odd extensions of the functions f(x)=xx+sinx+xex, where x(0, 1)g(x)=cos|x|+x2-x, where x(0, 1) respectively to the interval (-1, 0), then F(x)+G(x)  in (-1, 0) is:

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Important Questions on Functions

HARD
Mathematics
IMPORTANT
Let fx=x1+x and let gx=rx1-x. Then the number of value(s) of r is such that f(g(x))=g(f(x)) for infinitely many real numbers x is
HARD
Mathematics
IMPORTANT
If fx=x2+x+34 and gx=x2+ax+1 be two real functions, then the range of a for which gfx=0 has no real solution, is
HARD
Mathematics
IMPORTANT
If fx=-x+1,x0-x-12,x1 then the number of solution(s) of fx-f-1x=0 is
HARD
Mathematics
IMPORTANT
The function fx=cos-12[|sinx|+|cosx|]sin2x+2sinx+114 is defined if x belongs to (where · represents the greatest integer function):
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: