F(X)=|cos​-1(sgn x)| / cos-1(sgn x) then which of the following is (are) not correct?
​​a) range of f(x) contains no integer
​b)graph of f(x) is symmetric about y-axis
c)the equation f(x)=0 has two distinct real solutions
​d) inverse of f(x) is not defined

Dear Student,
Please find below the solution to the asked query:

Fx=cos-1sgnxcos-1sgnxRange of sgn x is -1,0,1, for x<0, x=0 and x>0 respectivelyAnd as cos-11=0 and denominator cannot be 0, henceFx is not defined when x>0F0= cos-10cos-10=π/2π/2=1For x<0Fx=ππ=1Hence range of fx is 1 for x0 and it is undefined for x>0As Fx=1 for all x0, hence it is many-one.F-1x does not exist...OptionD

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