If `f(x)={x^2 +2, x leq 2 and 1-x , x lt 2 and g(x)={2x ,x lt 1 and 3-x , x leq 1` ,evaluate `lim_(x->1) f(g(x))`.

If f(x)={(x^2+2,,,xge2),(1-x ,,,xlt2):} ; g(x)={(2x,,,xgt1),(3-x ,,,xle1):} then the value of lim_(x->1) f(g(x)) is

If f(x)={(x^2+2,,,xge2),(1-x ,,,xlt2):} ; g(x)={(2x,,,xgt1),(3-x ,,,xle1):} then the value of lim_(x->1) f(g(x)) is

x2 +2, X22If f(x) = { 2x , xgt1 11-x, xlt2 and g(x) = 3-, X51' 1. evaluate lim f(g(x)).

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

f(x)={x+2, 0lt=x<2 and 6-x , xgeq2 and g(x)={1+tanx , 0 leq x lt pi/4 and 3-cotx , pi/4 leq x lt pi . find fog and discuss the continuity and differentiabillity of fog.

Let f(x)={1-|x|,|x| leq 1 and 0,|x| lt 1 and g(x)=f(x-)+f(x + 1) , for all x in R .Then,the value of int_-3^3 g(x)dx is

Let f(x)={1-|x|,|x| leq 1 and 0,|x| lt 1 and g(x)=f(x-1)+f(x + 1) , for all x in R .Then,the value of int_-3^3 g(x)dx is

If f(x) = {sinx , x lt 0 and cosx-|x-1| , x leq 0 then g(x) = f(|x|) is non-differentiable for

If function defined by f(x) ={(x-m)/(|x-m|) , x leq 0 and 2x^2+3ax+b , 0 lt x lt 1 and m^2x+b-2 , x leq 1 , is continuous and differentiable everywhere ,

If the function f(x) ={x+1 if x le 1 , 2x+1 if 1 lt x le 2 and g(x) = {x^2 if -1 le x le 2 , x+2 if 2 le x le 3 then the number of roots of the equation f(g(x))=2