Q. Let `f:RR->RR` be a function such that `f(x+y)+f(x-y)=f(xy)` for all `x,y in RR` then `f` is`:` (A) Strictly increasing.(B). Strictly decreasing (C). Identically zero. (D). Constant but not necessarily zero.

If f:RR-> RR is a differentiable function such that f(x) > 2f(x) for all x in RR and f(0)=1, then

If f:RR-> RR is a differentiable function such that f(x) > 2f(x) for all x in RR and f(0)=1, then

If the function f: R to R is defined by f(x) =(x^(2)+1)^(35) for all x in RR then f is

If the function f satisfies the reation f(x+y)+f(x-y)=2f(x) f(y) Aax,yin RR and f(0) ne 0 then ____

Let f: RR rarr RR be a function defined by f(x)=ax+b , for all x in RR . If (f o f)=I_(RR) Find the value of a and b.

Let f, g are differentiable function such that g(x)=f(x)-x is strictly increasing function, then the function F(x)=f(x)-x+x^(3) is (A) strictly increasing AA x in R (B) strictly decreasing AA x in R (C) strictly decreasing on (-oo,(1)/(sqrt(3))) and strictly increasing on ((1)/(sqrt(3)),oo) (D) strictly increasing on (-oo,(1)/(sqrt(3))) and strictly decreasing on ((1)/(sqrt(3)),oo)

The number or linear functions f satisfying f(x+f(x))=x+f(x) AA x in RR is

The number or linear functions f satisfying f(x+f(x))=x+f(x) AA x in RR is

The number or linear functions f satisfying f(x+f(x))=x+f(x) AA x in RR is

The number or linear functions f satisfying f(x+f(x))=x+f(x) AA x in RR is