Show that the function `f(x)={x-1\ \ \ ,\ \ \ if\ x<2 2x-3\ \ \ ,\ \ \ if\ xgeq2` is not differentiable at `x=2` .

Show that the function f(x)=|x+1|+|x-1| for all x in R, is not differentiable at x=-1 and x=1

Show that the function f(x) = (x-2)/(x+1), x ne -1 is increasing.

Show that the functions f(x)=x^(2)-x+1, x ge 1/2 and phi(x)=1/2+sqrt(x-3/4) and mutually inverse and solve the equation x^(2)-x+1=1/2 +sqrt(x-3/4) .

Show that the function f(x)={:{(1-x", " x lt1),(x^2-1 ", " x ge 1):} is continuous but not differnetiable at x=1

Show that the function f(x)={((x^2sin(1/x),if,x!=0),(0,if,x=0)) is differentiable at x=0 and f'(0)=0

Show that the function f(x)={:{(1+x ", " x le2","),(5-x", "x gt2):} is not differentiable at x=2

Show tha the function f (x) = {{:(1+x"," if x le 2 ,), ( 5-x "," if x gt 2):} is not differentiable at x = 2 .

Show that the function f(x)={x^2sin(1/x),ifx!=0 0,ifx=0 is differentiable at x=0 and f^(prime)(0)=0

Show that the function f:R rarr R:f(x)={1 if x is rational and -1, if x is irrational is many- one into

Show that the function f(x)={|2x-3|[x]x 0 is continuous but not differentiable at x=1