Let `f:R->R` be such that for all `x in R`, `(2^(1+x)+2^(1-x))`,`f(x)` and `(3^x+3^(-x))` are in A.P. , then the minimum value of `f(x)` is :

Let F:R to R be such that F for all x in R (2^(1+x)+2^(1-x)), F(x) and (3^(x)+3^(-x)) are in A.P., then the minimum value of F(x) is:

Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f(y)+4^(y)f(x) AA x , y in R. The minimum value of f(x) is

Let f(x) = (x)/(1+|x|), x in R , then f is

Let f:R to R such that f(x+y)+f(x-y)=2f(x)f(y) for all x,y in R . Then,

Let R be the set of real numbers and f : R to R be such that for all x and y in R, |f(x) -f(y)|^(2) le (x-y)^(3) . Prove that f(x) is a constant.

Let f:(0,oo)->R be a differentiable function such that f'(x)=2-f(x)/x for all x in (0,oo) and f(1)=1 , then

Let f:R->R be a function defined by f(x)=x^2-(x^2)/(1+x^2) . Then:

Let y = f (x) such that xy = x+y +1, x in R-{1} and g (x) =x f (x) The minimum value of g (x) is:

Let f: R->R be defined as f(x)=(2x-3)/4 . Write fof^(-1)(1) .

Let f:[1,2] to [0,oo) be a continuous function such that f(x)=f(1-x) for all x in [-1,2]. Let R_(1)=int_(-1)^(2) xf(x) dx, and R_(2) be the area of the region bounded by y=f(x),x=-1,x=2 and the x-axis . Then,