[" If "|f(x_(1))-f(x_(2))|<(x_(1)-x_(2))^(2)," for all "x_(1),x_(2)in R.],[" point "(1,2).]

If f(x)=log((1+x)/(1-x)), then f(x) is (i) Even Function (ii) f(x_(1))-f(x_(2))=f(x_(1)+x_(2)) (iii) ((f(x_(1)))/(f(x_(2))))=f(x_(1)-x_(2)) (iv) Odd function

Statement 1: f(x)=(cos^(-1)x)^(2)+(pi)/2sin^(-1)x then Range of f(x) is [(3pi^(2))/16,3/4pi^(2)] Statement 2: If f(x)=ax^(2)+bx+c and if x_(1)lt(-b)/(2a)ltx_(2) then Range of f(x) in the interval [x_(1),x_(2)] is ["min"{f(x_(1)),f(x_(2)),f(-b/(2a))},"max"{f(x_(1)),f(x_(2)),f(-b/(2a))}]

If f(x_(1)-x_(2)),f(x_(1))f(x_(2)) & f(x_(1)+x_(2)) are in A.P. for all x_(1),x_(2) and f(0)!=0 then

Let x _(1) , x _(2), x _(3) be the points where f (x) = | 1-|x-4||, x in R is not differentiable then f (x_(1))+ f(x _(2)) + f (x _(3))=

Let x _(1) , x _(2), x _(3) be the points where f (x) = | 1-|x-4||, x in R is not differentiable then f (x_(1))+ f(x _(2)) + f (x _(3))=

Let f(x) and g(x) be two continuous functions defined from R rarr R, such that f(x_(1))>f(x_(2)) and g(x_(1)) f(g(3 alpha-4))

If F(x) is the probability function of a random varible X and X can assume only two values x_(1),x_(2) then the value of F(x_(1))+f(x_(2)) is

f(x) = log((1+x)/(1-x)) satisfies the equation: f(x_(1)) +f(x_(2))