Let `f(x)={:{(4, :, x lt-1),(-4x,:,-1 lex le 0):}`. If f(x) is an even function in R, then the defination of `f(x) " in " (0, +oo)` is :

f(x)={(4, xlt-1) ,(-4x,-1lt=xlt=0):} If f(x) is an even function in R then the definition of f(x) in (0,oo) is: (A) f(x)={(4x, 0ltxle1),(4, xgt1):} (B) f(x)={(4x, 0ltxle1),(-4, xgt1):} (C) f(x)={(4, 0ltxle1),(4x, xgt1):} (D) f(x)={(4, xlt-1),(-4x, -1lexle0):}

f(x)={(4, xlt-1) ,(-4x,-1lt=xlt=0):} If f(x) is an even function in R then the definition of f(x) in (0,oo) is: (A) f(x)={(4x, 0ltxle1),(4, xgt1):} (B) f(x)={(4x, 0ltxle1),(-4, xgt1):} (C) f(x)={(4, 0ltxle1),(4x, xgt1):} (D) f(x)={(4, xlt-1),(-4x, -1lexle0):}

Let f (x)= {{:(a-3x,,, -2 le x lt 0),( 4x+-3,,, 0 le x lt 1):},if f (x) has smallest valueat x=0, then range of a, is

Let f (x)= {{:(a-3x,,, -2 le x lt 0),( 4x+-3,,, 0 le x lt 1):},if f (x) has smallest valueat x=0, then range of a, is

Let f be an even function defined on R. Suppose f is defined on [0,4] as follows: f(x) = {{:(3x, if, 0 le x lt 1),(4-x, if, 1 le x le 4):} and f satisfies the condition. f(x-2) = f{x + [(6x^(2) + 272)/(x^(2) + 2)]) AA x in R Where [x] = greatest integer le x . Then f(3271) +f(-2052) + f(806) =..............

Let f (x) be defined as f (x) ={{:(|x|, 0 le x lt1),(|x-1|+|x-2|, 1 le x lt2),(|x-3|, 2 le x lt 3):} The range of function g (x)= sin (7 (f (x)) is :

Let f (x) be defined as f (x) ={{:(|x|, 0 le x lt1),(|x-1|+|x-2|, 1 le x lt2),(|x-3|, 2 le x lt 3):} The range of function g (x)= sin (7 (f (x)) is :

Let f(x) lt 0 AA x in (-oo, 0) and f (x) gt 0 ,AA x in (0,oo) also f (0)=0, Again f'(x) lt 0 ,AA x in (-oo, -1) and f '(x) gt 0, AA x in (-1,oo) also f '(-1)=0 given lim _(x to -oo) f (x)=0 and lim _(x to oo) f (x)=oo and function is twice differentiable. If f'(x) lt 0 AA x in (0,oo)and f'(0)=1 then number of solutions of equation f (x)=x ^(2) is : (a) 1 (b) 2 (c) 3 (d) 4