Let `g(x)=f(x)-1.` If `f(x)+f(1-x)=2AAx in R ,` then `g(x)` is symmetrical about. (a)The origin (b) the line`x=1/2` (c) the point (1,0) (d) the point `(1/2,0)`

Let g(x)=f(x)+f(1-x) and f''(x)<0 , when x in (0,1) . Then f(x) is

Let g(x)=2f(x/2)+f(1-x) and f^(primeprime)(x)<0 in 0<=x<=1 then g(x)

Let f(x)=x+f(x-1) for AAx in R . If f(0)=1,f i n d \ f(100) .

Let g(x)=f(x)+f(1-x) and f''(x)>0AAx in (0,1)dot Find the intervals of increase and decrease of g(x)dot

Let g(x)=2f(x/2)+f(2-x)a n df^('')(x)<0AAx in (0,2)dot Then g(x) increases in (a) (1/2,2) (b) (4/3,2) (c) (0,2) (d) (0,4/3)

If (f(x))^(2)xxf((1-x)/(1+x))=64x AAx in D_(f), then The domain of f(x) is

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1 +x) then (1) g(x) is an odd function (2) g(x) is an even function (3) graph of f(x) is symmetrical about the line x= 1 (4) f'(1)=0

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1 +x) then (1) g(x) is an odd function (2) g(x) is an even function (3) graph of f(x) is symmetrical about the line x= 1 (4) f'(1)=0

Let f(x)= sin^(-1)((2x)/(1+x^2))AAx in R . The function f(x) is continuous everywhere but not differentiable at x is/ are

Let f(x)=int x^2/((1+x^2)(1+sqrt(1+x^2)))dx and f(0)=0 then f(1) is