if `|f(x_1)-f(x_2)|<=(x_1-x_2)^2`Find the equation of gent to the curve `y= f(x)` at the 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

If f(x_(1))-f(x_(2))=f((x_(1)-x_(2))/(1-x_(1)x_(2))) for x_(1),x_(2)in(-1,1), then what is f(x) equal to? (a) In((1-x)/(1+x)) (b) In((2+x)/(1-x))(c)tan^(-1)((1-x)/(1+x))(d)tan^(-1)((1+x)/(1-x))

Statement -1 If f(x) and both are one one and f(g(x)) exists, then f(g(x)) is also one one. Statement -2 If f(x_(1))=f(x_(2))hArrx_(1)=x_(2) , then f(x) is one-one.

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 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))