Show that the function `f(x)={|2x-3|\ [x],\ \ \ xgeq1sin((pix)/2),\ \ \ \ \ \ x<1` is continuous but not differentiable at `x=1` .

Show that the function f(x)={|2x-3|\ [x],\ \ xgeq1; \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ sin((pix)/2),\ \ \ x<1 is continuous at x=1 .

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

Show that f(x) = {:{(|2x-3|[x],xge1),(sin((pix)/(2)), x <1):} is continuous but not differentiable at x =1.

Show that f(x)={{:(|2x-3|[x]", "xge1),(sin((pix)/2)", "xlt1):} is continuous but not differentiable at x = 1.

Discuss the continuity and differentiability in [ 0,2] of f(x)={|2x-3|[x], xgeq1 sin((pix)/2), x<1 to where [.] denotes the greatest integer function.

Discuss the continuity of the function f(x) given by f(x)={2-x ;\ \ \ x<2 2+x ;\ \ \ xgeq2 at x=2 .

Find the inverse of the function: f(x)={x^3-1, ,x<2x^2+3,xgeq2

Find the inverse of the function: f(x)={x^3-1, ,x<2x^2+3,xgeq2

Show that the function defined by f(x)= sin (x^(2)) is a continuous function