Let `f(x)={(x/tanx,;-ooltxlt0),(2,;x=0),(ln(1+2x)/x,;0ltxltoo):}` and `g(x)={(x+4,;-ooltxlt1),(x^2-5x+11,;1lexlt2),(x-3,;2lexltoo):}` then which of the following is correct?

If f(x)={(4, -3ltxlt-1),(5+x, -1lexlt0),(5-x, 0 lexlt2),(x^2+x-3, 2lexlt3):} then f(IxI) is

Let Y=(log(x+1)(x^(2)-3x+2)x^(2))/((x-4)^(3)(x+5)(x-3)(x^(2)+2x+2)) then which of the following options is correct

If f(x)={(x[x], 0lexlt2),((x-1)[x],2lexle3):} , then f(x) is

Let f(x)={{:(-3+|x|",",-ooltxlt1),(a+|2-x|",",1lexltoo):} and g(x)={{:(2-|-x|",",-ooltxlt2),(-b+"sgn(x),",2lexltoo):} where sgn(x) denotes signum function of x. If h(x)=f(x)+g(x) is discontinuous at exactly one point, then which of the following is not possible?

If f(x)={{:((x)/(sinx)",",x gt0),(2-x",",xle0):}andg(x)={{:(x+3",",xlt1),(x^(2)-2x-2",",1lexlt2),(x-5",",xge2):} Then the value of lim_(xrarr0) g(f(x))

If f(x)={{:((x)/(sinx)",",x gt0),(2-x",",xle0):}andg(x)={{:(x+3",",xlt1),(x^(2)-2x-2",",1lexlt2),(x-5",",xge2):} Then the value of lim_(xrarr0) g(f(x))

If f(x)={{:((x)/(sinx)",",x gt0),(2-x",",xle0):}andg(x)={{:(x+3",",xlt1),(x^(2)-2x-2",",1lexlt2),(x-5",",xge2):} Then the value of lim_(xrarr0) g(f(x))

Let f(x)={{:(x+1", "xlgt0),(2-x", "xle0):}"and"g(x)={{:(x+3", "xlt1),(x^(2)-2x-2", "1lexlt2),(x-5", "xge2):} Find the LHL and RHL of g(f(x)) at x=0 and, hence, find lim_(xto0) g(f(x)).

Let f(x)={{:(x+1", "xlgt0),(2-x", "xle0):}"and"g(x)={{:(x+3", "xlt1),(x^(2)-2x-2", "1lexlt2),(x-5", "xge2):} Find the LHL and RHL of g(f(x)) at x=0 and, hence, find lim_(xto0) g(f(x)).

Let f (x) be a continous function in [-1,1] such that f (x)= [{:((ln (ax ^(2)+ bx +c))/(x ^(2)),,, -1 le x lt 0),(1 ,,, x =0),((sin (e ^(x ^(2))-1))/(x ^(2)),,, 0 lt x le 1):} Then which of the following is/are corrent