If `f(x)+f(1-x)=2` and `g(x)=f(x)-1AAx in R ,` then `g(x)` is symmetric about

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

If f(x)=(1)/((1-x)) and g(x)=f[f{f(x))} then g(x) is discontinuous at

Statement -1: f(x) is invertible function and f(f(x)) = x AA x in domain of f(x), then f(x) is symmetrical about the line y = x. Statement -2: f(x) and f^(-1)(x) are symmetrical about the line y = x.

Let f(x)=||x|-1|-1| and g(x)-(max f(t):x<=t<=x+1,x in R} The graph of g(x) is symmetrical about

Suppose f and g are differentiabel functions such that xg (f(x))f'(g (x))g '(x) =(g(x))g '(f(x)) f'(x) AA x in R and f is positive AA n in R. Also int _( 0)^(x) f (g(t )) dt =1/2 (1-e^(-2x))AA x in R, g (f(0))=1 and h (x) = (g(f (x)))/(f (g(x)))AA x in R. The graph of y =h (x) is symmetric with respect to line:

If f(x)=x^2 and g(x)=x^2+1 then: (f@g)(x)=(g@f)(x)=

If f(x)=|x-1| and g(x)=f(f(f(x))) then for x>2,g'(x)=

If f(x)=|x-1|" and "g(x)=f(f(f(x))) , then for xgt2,g'(x) is equal to

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2) (0) = 1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R . then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(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