If `f(x)={x^2,` when `x >= 1 x,` when `x < 1,` prove that `f(x),` is not differentiable at `x=1.`

A function f(x) is defined as follows : f(x)=x," when "x lt1 =x+1," when "x gt1 =3/2," when "x=1 Draw the graph of f(x) and examine its continuity at x=(1)/(2)and x=1.

If f(x)=x^(2)+1, when x!=1 and f(x)=3 when x=1, prove that f(x) is not continuous at x=1.

If f(x) = x when 0lexlt1 = 2 - x when 1lexle2 = x-x^(2)/2 when xgt2 , then f(1.5) =

Discuss the applicability of Rolles theorem on the function f(x)={x^(2)+1, when 0<=x<=1 and 3-x, when 1

Let f(x)=2x^2-3," when "x le2 =2x+1," when "2ltxle3 =(1)/(2x-1)," when "xgt3 Find f(0),f(3),f(-2),f(4),f(sqrt(2)) and f(e).

If f(x)= {(x^2,"when" ,xlt0),( x ," when", 0lexlt1),( 1/x ," when", x gt1):} F i n d : (i) . f(1//2) (ii) . f(-2) (iii) . f(1) (iv) . f(sqrt(3)) (v) . f(-sqrt(3))

f(x) = (|x-a|)/(x-a) , when x ne a, = 1 , when x = a, then :

If f(x)={(x,"when "0le x le 1),(2x-1,"when "x gt 1):} then -

If f(x)={(x,"when "0le x le 1),(2x-1,"when "x gt 1):} then -

Find the domain and range of the function: f(x) = {(x^(2),"when " x lt 0),(x,"when " 0 le x le 1),((1)/(x),"when " x gt 1):}