If `f(x) = {(|x-1|/(1-x) + a); x > 1, a+b; x=1, |x-1|/(1-x)+b ; x < 1` is continuous at `x=1` then `a and b` aren

If f(x)=log((1+x)/(1-x)),t h e n (a) f(x_1)f(x)=f(x_1+x_2) (b) f(x+2)-2f(x+1)+f(x)=0 (c) f(x)+f(x+1)=f(x^2+x) (d) f(x_1)+f(x_2)=f((x_1+x_2)/(1+x_1x_2))

If f(x)=(x-1)/(x+1) , then f(f(a x)) in terms of f(x) is equal to (a)(f(x)-1)/(a(f(x)-1)) (b) (f(x)+1)/(a(f(x)-1)) (f(x)-1)/(a(f(x)+1)) (d) (f(x)+1)/(a(f(x)+1))

If f(x)=(x-1)/(x+1) , then f(f(a x)) in terms of f(x) is equal to (a)(f(x)-1)/(a(f(x)-1)) (b) (f(x)+1)/(a(f(x)-1)) (f(x)-1)/(a(f(x)+1)) (d) (f(x)+1)/(a(f(x)+1))

If f(x)=log((1+x)/(1-x)),t h e n (a) f(x_1)f(x_2)=f(x_1+x_2) (b) f(x+2)-2f(x+1)+f(x)=0 (c) f(x)+f(x+1)=f(x^2+x) (d) f(x_1)+f(x_2)=f((x_1+x_2)/(1+x_1x_2))

If f(x)=log((1+x)/(1-x)),t h e n (a) f(x_1)f(x_2)=f(x_1+x_2) (b) f(x+2)-2f(x+1)+f(x)=0 (c) f(x)+f(x+1)=f(x^2+x) (d) f(x_1)+f(x_2)=f((x_1+x_2)/(1+x_1x_2))

Suppose f(x) = { (a+bx , x lt 1),(4 , x = 1), (b - ax , x gt 1) :} and if lim_(x rarr 1) f(x) = f(1) what are the possible values of a and b ?

{:(1.if F (X) = (1)/(x) then f'(1) =A, 2.If f (x) = (x+1)/(x+3) then f '(-1) =B),(3.If f(x)=x^(2)then f'(1)=C,4. If f(x)=logx then f'(3)=D):} The ascending order of A,B,C ,D is

If f(x)=(x-1)/(x+1), then f(f(ax)) in terms of f(x) is equal to (a) (f(x)-1)/(a(f(x)-1)) (b) (f(x)+1)/(a(f(x)-1))(c)(f(x)-1)/(a(f(x)+1))(d)(f(x)+1)/(a(f(x)+1))