Let `f(x)=1/(1+|x|)+1/(1+|x-1|)` for all `x in [-1,1].` Then. which one ot the Ilowing is true?

Let f(x) = |x-1| , then which of the following is true

Let f(x)={(x-1)sin1/(x-1)if\ x!=1 0,\ if\ x=1 . Then which one of the following is true? (a) f is differentiable at x=0\ and at \ x-1 (b) f is differentiable at x=0\ but not at \ x=1 (c) f is differentiable at x=0 nor at x=1 (d) f is differentiable at x=1\ but not at \ x=0

Let f(x)=x+(1)/(x) when x in (0,1) Then which one of the following is correct ?

Let f(x)={((x-1)^2 sin(1/(x-1))-|x|,; x != 1), (-1,; x=1):} then which one of the following is true?

Let f(x)={((x-1)^2 sin(1/(x-1))-|x|,; x != 1), (-1,; x=1):} then which one of the following is true?

Let F(x)={(x-1)(sin1)/(x-1),x!=1,{0,x=1 then which one of the following is true.

Let f(x)=(1-x)^(2) sin^(2) x+x^(2) for all x in RR , and let g(x)=int_(1)^(x) ((2(t-1))/(t+1)-log t)f(t) dt for all x in (1, oo) . Which of the following is true?