If `f(x)={x-2, x le 0 and 4-x^2,x > 0,` then discuss the continuity of `y=f(f(x)).`

Discuss the continuity of f(x)=sgn(x^2-2x+3)

Discuss the continuity of f(x)=(log|x|)sgn(x^2-1),x!=0.

Discuss the continuity of f(x)={(x^2)/(|x|),x!=0 0,x=0

Discuss the continuity of f(x)={1/(e^(x-1)),x!=1 0,x=1

Let f(x)={(1+3x)^(1/x), x != 0e^3,x=0 Discuss the continuity of f(x) at (a) x=0, (b) x=1

f(x) = x^2 +1 ,0 le x le 2 find the range of the function f.

Let f(x)=2x(2-x), 0 le x le 2 . Then find the number of solutions of f(f(f(x)))= (x)/(2) .

if f(x)={x^3 x<0 3a+x^2 x≥0 is continuous at x = 0 , then a is

if f(x) = {(x^(3),x <0),(3a + x^(2), x ge 0):} is continuous at x = 0 , then a is

If f(x)={x+1/2, x<0 2x+3/4,x >=0 , then [(lim)_(x->0)f(x)]= (where [.] denotes the greatest integer function)