Show that the function f(x) = |x| is even.

Show that the function f(x) = 2x+9 is one-one.

Show that the function f(x) = {:{(|x|, x le2),([x],x>2):} is continouous on [0,2]

Show that the function f(x) = |x + 1| + | x - 1| is continuous at x = -1 , x = 1

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

Show that the function f(x) = |sin x + cos x | is continuous at x = pi .

Show that the function f (x) = (x)/(1+|x|) is a strict increasing function.

Show that the function f(x) = x -(1)/(x) is a strict increasing function fox x > 0

Show that the function f(x) = {{:(x^2 + 3 , "if" x != 0),(1,"if" x = 0):} is not continous at x = 0 .

Show that the function f(x) = {{:(-x^2, x le 0),(x^2 ,x gt 0):} is continuous at x = 0 . Also show that f is differentiable at x = 0 .