Test the continuity of `f(x)`, where `f(x)={x^2+x+1, 0 leq x leq 1 and x^2+2 , 1 lt x leq 2`

Let f(x)=1+x , 0 leq x leq 2 and f(x)=3−x , 2 lt x leq 3 . Find f(f(x)) .

Examine the continuity of f(x) at x=1/2 where f(x)={{:(1/2-x", "0lexlt1/2),(1", "x=1/2),(3/2-x", "1/2ltxle1):}

Discuss the continuity of the function f(x) at x = 1/2 where f(x) = {{:(1/2 + x"," , x le x lt 1/2),(1",", x = 1/2),(3/2 + x,1/2 lt x lt 1):}

Test the continuity of f(x) at x=0 where f(x)=(1)/(1+2^((1)/(tau))) when x!=0;f(x)=1 when x=0

Check the continuity of the function f defined by f(x)={{:(x+1,if xle1),(2x,if 1 lt x lt 2x),(1+xA^(2),if x ge 2):} at x=1 and 2

If f(x) is continuous at x=0 , where f(x)={:{(x^(2)+1", for " x ge 0),(2sqrt(x^(2)+1)+k ", for " x lt 0):} , then k=

Discuss the continuity of the function f, where f is defined by f(x)={{:(-2," if "x le -1),(2x," if "-1 lt x le 1),(2," if "x gt 1):} .

Discuss the continuity of the function f, where f is defined by f(x)={{:(-2," if "x le -1),(2x," if "-1 lt x le 1),(2," if "x gt 1):} .