[f(x)={[-x,,x<1],[a+cos^(-1)(x+b),,1leqslant x leqslant2]],[" differentiable at "x=1," then "(a)/(b)" is equal to: "]

If f(x)=-x|x| ,then f^(-1)(x) is :

If f(x)=-x|x| , then f^(-1)(x) is :

If f(x) =|x|, x in R , then

In which of the following function, range is not singleton set f(x)=[x]+[-x] (b) f(x)={x}+{-x} f(x)=|sgn(x)| (d) f(x)=[sqrt(x-[x]) where [x],{x},a n dsgn(x) are greatest integer function, fractional part function and signum function respectively.

In which of the following function,range is not singleton set f(x)=[x]+[-x]( b) f(x)={x}+{-x}f(x)=|sgn(x)|(d)f(x)=[sqrt(x-[x]) where [x],{x}, and sgn(x) are greatest integer function,fractional part function and signum function respectively.

The function f(x)=x-|x-x^(2)| is

Find the value of f'(x) when f(x)=|x|(x+|x|)

If f(x)=x -|x| is

The number or linear functions f satisfying f(x+f(x))=x+f(x) AA x in RR is