Let `f(x)={1+x ,0 lt x leq 2 and 3-x ,2 lt x leq 3` Determine the composite function `g(x) = f(f(x))` & hence find the point of discontinuity of g. if any.

Let f(x)={(1+x, 0 le x le 2), (3-x, 2 lt x lt 3):} Determine the form of g(x) = f[f(x)] and hence find the points of discontinuity of g, if any.

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

If the function f(x)= (1)/(x+2) , then find the points of discontinuity of the composite function y= f {f(x)}

if f(x) = {:{ (1+x, ,0 le x le2), (3-x, ,2 lt x le3):} Determine the points of discontinuity of the function f (f(x)) (ii) Check the continuity of the function f(x) = [x]^(2) - [x^(2)] (iii) find the values of a and b if f is continuous at x = pi/2 f(x)= {:{((8/5)""^(tan8x)/(tan 5x) , , 0 lt x lt pi//2),(a+4, , x=pi//2), ((1+|cot x|)""^(b|tan x|)/a, , pi/2 lt x lt pi):}

If alpha, beta (where alpha lt beta ) are the points of discontinuity of the function g(x) = f(f(f(x))), where f(x) = (1)/(1-x). Then, The points of discontinuity of g(x) is

If alpha, beta (where alpha lt beta ) are the points of discontinuity of the function g(x) = f(f(f(x))), where f(x) = (1)/(1-x) . Then, The points of discontinuity of g(x) is

f(x) = 1 + [cosx]x in 0 leq x leq pi/2 (where [.] denotes greatest integer function) then

If f(x) = sgn (x) and g (x) = (1-x^2) ,then the number of points of discontinuity of function f (g (x)) is -

If f(x)=sgn(x-2) xx [In x], 1leq x leq 3 and {x^2} ,-3 lt x leq 3.5 where [.] denotes the greatest integer function and {.} represents the fractional part functon, then the number of points of discontinuity in [1,3.5] is

If f: x: -1 leq x leq 1 -> {x : -1 leq x leq 1} , then which is/are bijective