Prove that f (x) = |x-1|,x in R is not differnentiable at x=1

Prove that f (x) =|x| is continuous at x =0

Prove that f (x) = [X] is discontinuous for integral values of x.

if f(x)={(x^2,xle1),(ax+b,x>1):} is differentiable at x = 1, find the values of a and b. Hence find f'(1)

Prove that f : R rarr R, f(x)=4x-5 is invertible and find f^-1(x) .

Prove that f(x) = sin x and f(x) = cos x are continuous.

Prove that x+1/x=sintheta is not possible for all x in R

Prove that the identity function f(x) = x is continous

Does f'(1) exist if f(x) = |x-1|+|x+1|

Prove that log_a x+log_(1/a) x=0

Show that f(x)=e^(1//x) is a strictly decreasing function for all x in R .