If `f(x) = |x|` then show that `f'(2) =1`

If f(x) = 2/(2-x) then show that f(f(f(x))) = (2(x-1))/x

If f(x)=(x-1)/(x+1), then show that f((1)/(x))=-f(x) (ii) f(-(1)/(x))=(1)/(f(x))

If f(x)=(x-1)/(x+1) then show that f(1/x)=-f(x) and f(-1/x)=(-1)/f(x)

A=[[1,22,1]] and f(x)=x^(2)-2x-3 then show that f(A),=0

f(x)=(2x+3)/(3x+2), then show that f(x)*f((1)/(x))=1. if f(x)=4, then show that f(x+1)-f(x)=f(x)

Let f defined on [0,1] be twice differentiable such that |f(x)|<=1 for x in[0,1], if f(0)=f(1) then show that |f'(x)<1 for all x in[0,1]

If f(x)=1+x+x^(2)+..... for |x|lt1 then show that f^(-1)(x)=(x-1)/(x)