Statement-1: If `|f(x)| le |x|` for all `x in R` then `|f(x)|` is continuous at 0. Statement-2: If `f(x)` is continuous then `|f(x)|` is also continuous.

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

The contrapositive of statement: If f(x) is continuous at x=a then f(x) is differentiable at x=a

Statement I f(x) = sin x + [x] is discontinuous at x = 0. Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.

Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is continuous at x=0, show that f(x) is continuous for all xdot

Show that the function f(x)=2x-|x| is continuous at x=0.

Show that the function f(x)=2x-|x| is continuous at x=0 .

Leg f(x+y)=f(x)+f(y)fora l lx , y in R , If f(x) is continue at x=0,s howt h a tf(x) is continuous at all xdot

Let f(x) = sin"" 1/x, x ne 0 Then f(x) can be continuous at x =0

Statement-1 : f(x) = x^(7) + x^(6) - x^(5) + 3 is an onto function. and Statement -2 : f(x) is a continuous function.

If f.g is continuous at x = 0 , then f and g are separately continuous at x = 0 .